Assembly System

Abstract

Disclosed embodiments relate to assembly systems and methods, such as systems and methods for installing objects using multiple tethers. An apparatus and method are disclosed for installing a first object into a chamfered cavity of a second object. In some embodiments, the first object is suspended from multiple flexible tethers such that the flexible tethers hold the first object in a suitable orientation for insertion into the second object. Assembly apparatus according to the present disclosure can be used in any suitable application. For example, in some embodiments, the assembly apparatus may be attached to or otherwise part of a gantry crane assembly, a crane, or other support structure for installing the first object into the cavity of the second object.

Description

[Technical Field]

[0001] (CROSS-REFERENCE TO RELATED APPLICATIONS) This application claims the benefit under 35 U.S.C. Section 119(e) of U.S. Provisional Patent Application No. 63 / 012,363, filed April 20, 2020, and entitled "Apparatus and Method of Precision Assembly of Objects Suspended with Multiple Cables," which is incorporated herein by reference in its entirety.

[0002] The disclosed embodiments relate to assembly systems and methods, for example, systems and methods for installing objects using multiple tethers. [Background technology]

[0003] When assembling objects in heavy industries (e.g., aerospace, shipbuilding, mining, etc.), heavy workpieces and subassemblies may need to be precisely positioned relative to other objects and / or structures. Typically, the fine positioning and / or interlocking of objects suspended by a crane requires special training and / or experience, making typical object assembly highly dependent on skilled labor. Generally, assembly may be performed by a worker standing near the crane-suspended objects and adjusting the position and orientation of one or more objects by directly pushing and / or pulling the one or more objects while adjusting the height of the crane. Summary of the Invention [Means for solving the problem]

[0004] According to one aspect, an assembly apparatus includes a support structure; a plurality of tethers suspended from the support structure, the plurality of tethers configured to suspend a first object from the support structure; and one or more actuators operably coupled to at least one selected from the group consisting of the support structure and the plurality of tethers, the one or more actuators configured to lower, under the influence of gravity, a portion of the first object toward a cavity formed in a second object with a chamfer formed along at least a portion of the cavity, the one or more actuators and the plurality of tethers configured to control the descent of the portion of the object such that the portion of the first object contacts and slides along the chamfer as the portion of the first object is inserted into the cavity.

[0005] According to another aspect, a method of installing an object in a cavity includes suspending a first object from a plurality of tethers of an assembly apparatus; lowering a portion of the first object under the influence of gravity toward a cavity formed in a second object with a chamfer formed along at least a portion of the cavity such that at least a portion of the first object contacts the chamfer; sliding a portion of the first object along the chamfer; and installing the first object in the cavity of the second object.

[0006] It should be understood that the foregoing concepts, and additional concepts discussed below, may be arranged in any suitable combination, as the disclosure is not limited in this respect. Furthermore, other advantages and novel features of the present disclosure will become apparent from the following detailed description of various non-limiting embodiments when considered in conjunction with the accompanying figures. The present specification also provides, for example, the following: (Item 1) 1. An assembly device comprising: a support structure; a plurality of tethers suspended from the support structure, the plurality of tethers configured to suspend a first object from the support structure; and one or more actuators operably coupled to at least one selected from the group of the support structure and the plurality of tethers, the one or more actuators configured to lower a portion of the first object under the influence of gravity toward a cavity formed in a second object with a chamfer formed along at least a portion of the cavity; Equipped with wherein the one or more actuators and the plurality of tethers are configured to control a descent of a portion of a first object such that the portion of the first object contacts and slides along the chamfer as the portion of the first object is inserted into the cavity. (Item 2) Item 1, wherein the one or more actuators are configured to maintain a predetermined tension within each tether of the plurality of tethers as a portion of the first object is lowered into the cavity. (Item 3) Item 1, wherein the one or more actuators are configured to lower the support structure. (Item 4) Item 4. The assembly apparatus of item 3, wherein the one or more actuators include a plurality of actuators configured to expand the plurality of tethers and lower the first object. (Item 5) Item 5. The assembly apparatus of item 4, wherein the plurality of tethers includes one or more sensors configured to sense tension in the plurality of tethers. (Item 6) Item 6. The assembly apparatus of item 5, wherein the one or more actuators are configured to modify tension in the plurality of tethers based, at least in part, on the sensed tension. (Item 7) 7. The assembly apparatus of claim 6, wherein the one or more actuators are configured to be controlled by a processor based, at least in part, on the sensed tension. (Item 8) Item 1, wherein the one or more actuators and the plurality of tethers are configured to maintain the first object in a substantially upright position while the first object is lowered into a cavity of the second object. (Item 9) Item 1, wherein the plurality of tethers includes two tethers configured to move the first object in two dimensions. (Item 10) Item 1, wherein the plurality of tethers includes three tethers configured to move the first object in three dimensions. (Item 11) Item 1, wherein the one or more actuators are configured to move the first object such that a magnitude of movement of the portion of the first object toward the cavity of the second object exceeds a magnitude of movement of the portion of the first object away from the cavity of the second object as the first object slides along the chamfer of the second object. (Item 12) Item 1, an assembly apparatus according to item 1, wherein lines extending coaxially with the plurality of tethers intersect at an intersection point, the intersection point being offset a predetermined distance in a vertical direction from a bottom surface of a portion of the first object oriented toward the cavity, the vertical direction being parallel to the direction of gravity. (Item 13) Item 13. The assembly apparatus of item 12, wherein the predetermined distance is offset from the bottom surface by at least 50% of the overall length of the first object, and the overall length is parallel to the direction of gravity. (Item 14) Item 13. The assembly apparatus of item 12, further comprising a processor configured to control the one or more actuators such that a length of each tether of the plurality of tethers is set such that the intersection is offset from the bottom surface by at least the predetermined distance. (Item 15) 1. A method of placing an object in a cavity, comprising: suspending a first object from a plurality of tethers of an assembly apparatus; lowering a portion of the first object under the influence of gravity toward a cavity formed in a second object with a chamfer formed along at least a portion of the cavity such that at least a portion of the first object contacts the chamfer; sliding a portion of the first object along the chamfer; placing the first object within the cavity of the second object; A method comprising: (Item 16) Item 16. The method of item 15, wherein lowering the first object into the cavity of the second object includes lowering the plurality of tethers. (Item 17) 17. The method of claim 16, wherein lowering the plurality of tethers includes maintaining a predetermined tension within each tether of the plurality of tethers as a portion of the first object is lowered into a cavity of the second object. (Item 18) Item 16. The method of item 15, wherein lowering the first object into the cavity includes maintaining the first object in a substantially upright position. (Item 19) Item 16. The method of item 15, wherein sliding the portion of the first object along the chamfered portion comprises moving the first object such that a magnitude of movement of the portion of the first object toward the cavity of the second object exceeds a magnitude of movement of the portion of the first object away from the cavity of the second object. (Item 20) Item 16. The method of item 15, wherein suspending the first object from a plurality of tethers of the assembly apparatus includes suspending the first object so that lines extending coaxially with the plurality of tethers intersect at an intersection point, the intersection point being offset a predetermined distance in a vertical direction from a bottom surface of a portion of the first object oriented toward the cavity, and the vertical direction being parallel to the direction of gravity. [Brief explanation of the drawings]

[0007] Non-limiting embodiments of the present disclosure will be described, by way of example, with reference to the accompanying drawings, which are schematic diagrams not intended to be drawn to scale. In the drawings, each identical or nearly identical component shown is typically represented by a single numeral. For purposes of clarity, not every component is labeled in every drawing, not every component of every embodiment of the present disclosure is shown, and the drawings do not necessarily enable those skilled in the art to understand the present disclosure.

[0008] [Figure 1] FIG. 1 is a front view of a passive assembly device, according to one illustrative embodiment. [Figure 2A] FIG. 2A is a front view of a suspended object contacting a chamfer in a cavity of a stationary object, according to an illustrative embodiment. [Figure 2B] FIG. 2B is a front view of a suspended object contacting one point on the interior wall of a cavity of a stationary object, according to an illustrative embodiment. [Figure 2C] FIG. 2C is a front view of a suspended object contacting two points on the interior wall of a cavity of a stationary object, according to an illustrative embodiment. [Figure 3A] FIG. 3A is a front view of an object suspended from multiple flexible tethers, according to one illustrative embodiment. [Figure 3B] FIG. 3B is a front view of an object suspended from multiple flexible tethers, according to another illustrative embodiment. [Figure 4] FIG. 4 is a front view of an active assembly device, according to an illustrative embodiment. [Figure 5] FIG. 5 is a flow chart illustrating a method for passively placing a first object within a cavity of a second object. [Figure 6]FIG. 6 is a flow chart illustrating a method for actively placing a first object within a cavity of a second object. [Figure 7] FIG. 7 is a front view of an exemplary assembly device, according to one illustrative embodiment. [Figure 8] FIG. 8 is a front view of an assembly device, according to an illustrative embodiment. [Figure 9] FIG. 9 is a graph showing the relationship between the coefficient of friction of the chamfer of the stationary object and the initial angle of the flexible tether of the assembly device, according to one experiment. [Figure 10] FIG. 10 is a graph showing the experimentally measured relationship between the initial angle of the flexible tether of the assembly apparatus and the depth at which two-point contact between a portion of the suspended object and the inner wall of the cavity of the stationary object can be achieved. [Figure 11] FIG. 11 is a graph showing the experimentally measured relationship between depth of travel and suspended object center / cavity center distance. [Figure 12] FIG. 12 is a graph illustrating the relationship between the coefficient of friction of a chamfer of a stationary object and the initial angle of a flexible tether, according to one embodiment. [Figure 13] FIG. 13 is a graph illustrating the relationship between the coefficient of friction of a chamfer of a stationary object, according to another embodiment. [Figure 14] FIG. 14 is a graph illustrating the relationship between the coefficient of friction of a chamfer of a stationary object, according to yet another embodiment. [Figure 15] Figure 15A is a front view of an exemplary assembly device, according to one illustrative embodiment. Figure 15B is a front view of a portion of the assembly device of Figure 15A contacting a surface and the resulting forces based on the location of the instantaneous center of rotation, according to one embodiment. Figure 15C is a front view of a portion of the assembly device of Figure 15A contacting a surface and the resulting forces based on the location of the instantaneous center of rotation, according to one embodiment. Figure 15D is a front view of a portion of the assembly device of Figure 15A contacting a surface and the resulting forces based on the location of the instantaneous center of rotation, according to one embodiment. Figure 15E is a front view of a portion of the assembly device of Figure 15A contacting a surface and the resulting forces based on the location of the instantaneous center of rotation, according to one embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0009] Detailed Description Assembling objects is a critical task in heavy industries (e.g., aerospace, shipbuilding, mining, etc.). To assemble such objects, precise positioning and / or installation of heavy (e.g., greater than 25 kg) workpieces and / or subassemblies relative to other workpieces and / or subassemblies may be desired, which can often prove to be a daunting task. Typically, fine positioning or engagement of a crane-suspended object can be particularly difficult. For example, a worker may assemble a heavy object by standing near the crane-suspended object and adjusting the object's position and / or orientation by directly pushing and / or pulling the object while adjusting the crane's height. The worker may firmly push a specific portion of the object so that the object's orientation can be aligned with a reference line without overshooting. In some cases, engaging a suspended object with a second object, such as a stationary structure, can be particularly difficult. The suspended object can be lowered with a defined position and orientation so that the object can be seated within the structure stably and with a high level of precision. This may involve workers adjusting cranes and lowering suspended objects while manipulating the location and / or orientation of the suspended object in a horizontal plane. Such high-precision assembly is employed in a wide variety of applications, including turbine generators, marine, and construction machinery and their components, including large transmissions and motors. To perform these operations quickly, workers may need to have many years of experience and / or substantial training.

[0010] In light of the above, the inventors have recognized advantages associated with constructs and systems that can help guide a suspended object into a desired position and / or orientation relative to a cavity of an object located vertically below the suspended object as the objects are interlocked with one another. Thus, in some embodiments, a first suspended object can be suspended from an assembly apparatus by multiple tethers. The first suspended object can then be lowered (e.g., by the assembly apparatus) toward a secondary stationary object under the influence of gravity. The second stationary object can then include a cavity for receiving the first suspended object with a chamfer extending at least partially around the perimeter of the cavity. The suspended object can be roughly positioned such that a portion of the first suspended object contacts the chamfer as the first suspended object is lowered toward the cavity. Once the first suspended object contacts the chamfer, movement of the first suspended object may be controlled such that the portion of the suspended object contacting the chamfer slides along the chamfer, at least partially inward along the chamfer surface, in a direction oriented toward the cavity. The first suspended object may then be placed within the cavity of the second stationary object once the object is received within the cavity. For example, in some embodiments, the first suspended object may slide along the chamfer toward the cavity before contacting the interior wall of the cavity at one point. After contacting the interior wall of the cavity at one point, the first suspended object may subsequently contact the interior wall of the cavity at a second point, stabilizing the first object within the cavity prior to being lowered further into the cavity.

[0011] To enable the desired functionality described above, in some embodiments, an assembly apparatus according to the present disclosure may include a support structure and a plurality of flexible tethers extending from the support structure. The plurality of flexible tethers may be configured to suspend a first object from the flexible tether in a desired orientation during insertion. Furthermore, in some embodiments, the plurality of tethers may be configured to maintain tension within each tether above a predetermined tension per tether as the first suspended object is lowered toward the cavity of the second stationary object. Depending on the particular embodiment, this may be due to the tethers having a predetermined length. However, in other embodiments, the tension within each of the tethers may be actively controlled by one or more actuators to maintain tension within each tether above the associated predetermined tension such that the first suspended object is oriented in a generally upright position as the first suspended object is lowered toward the cavity of the second stationary object and slides across the chamfered surface into the cavity.

[0012] Depending on the desired application and object geometry, the systems and methods disclosed herein can be used to orient and place an object within a cavity, either relative to a two-dimensional reference plane and / or within a three-dimensional environment.

[0013] In light of the above, in some embodiments, it may be desirable to maintain the orientation of a first suspended object relative to a cavity of a second, stationary object disposed vertically below the first suspended object in two dimensions (e.g., vertical and horizontal dimensions) that are perpendicular to one another. In such cases, the assembly apparatus may include at least two flexible tethers from which the first object may be suspended. The flexible tethers may serve to hold the first object in a desired orientation relative to the cavity while the first object is moved by the support structure and / or the tethers. In particular, the support structure may raise or lower the first object while the tethers maintain the orientation of the first object. Alternatively, or in addition, the flexible tethers may raise and / or lower the first object by modifying the length of the tethers, for example, by extending and / or retracting the tethers. In either case, the tether may be appropriately tensioned (e.g., actively or passively, as described in more detail herein) to maintain the desired orientation of the first object relative to the cavity both prior to and during insertion.

[0014] As described above, in some embodiments, it may be desirable to maintain the orientation of the first suspended object in three dimensions relative to three orthogonal axes. In such cases, the assembly apparatus may include at least three flexible tethers for properly positioning and maintaining the orientation of the first object in three-dimensional space (e.g., orthogonal X, Y, and Z axes). Tension in the tethers as the first suspended object is lowered into the cavity of the second object may be appropriately maintained and / or controlled to facilitate insertion of a portion of the first object into the cavity of the second object, as further detailed below.

[0015] In various embodiments described herein, including those described above, assembly devices including two and three tethers are described. However, it should be understood that an assembly device according to the present disclosure may include any suitable number of tethers, including four tethers, five tethers, six or more tethers, and / or any other suitable number of tethers may be used depending on the application. However, there may be advantages to using two tethers and three tethers to position an object in a two-dimensional reference plane and in three-dimensional space, respectively, due to the increased number of tethers, which increases the constraint of the suspended object during assembly.

[0016] In some cases, the assembly device may be capable of performing the insertion process (e.g., as described above) in any suitable manner. For example, in some embodiments, the insertion process is performed passively. In such embodiments, the assembly device is configured such that the support structure is moved to move the object while maintaining a desired tension under gravity, such that a tether connected to the support structure controls the orientation of the object as it is inserted into the cavity. For example, in such embodiments, a first object may be suspended from a tether with a fixed length configured to control the object's motion relative to the cavity as the object is lowered. To lower the object, the support structure may also be lowered, which lowers the tether and, therefore, the first object. Such functionality may be performed using a crane, a movable gantry arrangement, or any other suitable system capable of controlling the vertical displacement of the support structure and connected object, depending on the application.

[0017] Alternatively or additionally, in some cases, the assembly device may be capable of actively controlling the insertion process. In particular, in some embodiments, the tension and / or length associated with each of the flexible tethers may be actively controlled using one or more actuators operably coupled to the tethers while the assembly device is inserting a first object into a cavity of a second object. For example, the tethers may be connected to displaceable arms, actuated tether reels, or other actuated systems capable of manipulating the length and / or tension of the tethers extending out from the support structure to which they are connected. In some embodiments, the length and / or tension of each tether of multiple tethers may be independently controlled, which may allow the assembly device to be adapted to suit a variety of applications. As will be understood by those skilled in the art, the tethers may be actively controlled in any suitable manner during insertion, depending on the application and as described in more detail below.

[0018] In some cases, it may be desirable for the active control of each tether to be automated. For example, the active control of the tethers may be performed by a processor. In such embodiments, one or more processors may be operatively coupled to one or more actuators associated with the multiple tethers and control the operation of the one or more actuators. Specifically, the one or more processors may be configured to control one or more parameters (e.g., length and / or tension) of the tethers. In some embodiments, this may include active feedback control. For example, one or more sensors may be configured to sense the tension and / or length of each tether. In some embodiments, this may correspond to a separate sensor associated with each tether. In either case, a signal associated with the sensed parameter may be output to the one or more processors. The one or more processors may then control the tension and / or length of the multiple tethers based, at least in part, on the sensed parameter obtained from the one or more sensors.

[0019] The assembly device may employ any suitable type of sensor for sensing the parameters described above. For example, tension applied to a tether of the assembly device may include one or more of a load cell, force sensor, extensometer, strain gauge, and / or any other suitable sensor configured to sense the tension or load applied to an associated tether. With respect to the expansion of one or more tethers, suitable sensors may include, without limitation, an actuator encoder and / or any other suitable type of sensor configured to sense or otherwise determine the length of the associated tether extending out from the corresponding support structure. Of course, while specific sensors are described above, as will be understood by one of ordinary skill in the art, any suitable sensor or combination of sensors may be employed with the disclosed system, as the disclosure is not limited in this manner.

[0020] In some embodiments, the flexible tether may be angled relative to the horizontal plane of the suspended object (e.g., a plane perpendicular to the direction of gravity) in any suitable manner. It should be understood that the range of such appropriate angles may be based, at least in part, on the geometry of the object suspended from the tether. In particular, the angle may be set so that the suspended object may be oriented to limit the extent to which the suspended object may move toward and / or enter a cavity in the stationary object (e.g., along a chamfer) and tilt while transitioning toward a two-point contact state (e.g., as described in more detail herein). In some cases, configuring the tether with an appropriate angle may serve to prevent the suspended object from becoming stuck and / or binding within the cavity and / or along the chamfer.

[0021] In light of the above, the angle may be set such that the flexible tether can instantaneously rotate the suspended object about a predetermined rotation point in an attempt to prevent binding and / or adhesion. Without wishing to be bound by theory, the suspended object may tend to rotate about an instantaneous center of rotation defined by an imaginary point where lines parallel to and coaxial with the tether intersect with each other. To prevent binding and / or adhesion, the instantaneous center of rotation may be located above or below the lower surface of the suspended object (e.g., the surface oriented toward the cavity of the stationary object) by a predetermined distance.

[0022] Depending on the geometry of the suspended object, the angle of the tether relative to a plane perpendicular to the direction of gravity can be any suitable value depending on the desired application, as detailed below for some configurations. Specifically, due to undesirable adhesion and / or stationary behavior that occurs over a range of tether angles, there may be both an upper and a lower preferred range of angles over which the application will occur. In particular, longer suspended objects may allow for a larger range of suitable angles, while shorter objects may have a smaller range of suitable angles. Exemplary ranges that may be used in some applications are provided below.

[0023] In some embodiments, the tethers of the assembly device may exhibit suitable tether angles (e.g., angles formed between the tether and a plane perpendicular to the direction of gravity) over a first operating range of angles to avoid sticking and / or stationary behavior of the object during insertion. These tether angles may be less than or equal to 90 degrees, 85 degrees, 80 degrees, and / or any other suitable angle. Correspondingly, the tethers of the assembly device may have suitable tether angle ranges greater than or equal to 75 degrees, 80 degrees, 85 degrees, and / or any other suitable angle. Combinations of the above-described ranges are also contemplated, including, but not limited to, angles between or equal to 75 degrees and 90 degrees. Of course, any suitable range of tether angles may be employed depending on the application.

[0024] Alternatively, or in addition, in some embodiments, the tethers of the assembly device may be arranged to operate within a second operating range of angles to avoid sticking and stationary behavior of the object during insertion. For example, depending on the geometry of the suspended object, a suitable tether angle range may be less than or equal to 70 degrees, 60 degrees, 50 degrees, and / or any other suitable angle. Correspondingly, the tethers of the assembly device may have tether angles greater than or equal to 1 degree, 10 degrees, 20 degrees, and / or another suitable angle. Combinations of the above-described ranges are also contemplated, including, without limitation, tether angles between or equal to 1 degree and 70 degrees. Of course, any suitable range of tether angles may be employed depending on the application.

[0025] In some embodiments, the tether angles may be set so that the tethers do not intersect when the suspended object is suspended from the tethers. Thus, in some embodiments, tether angles between or equal to about 0 degrees and 120 degrees are also contemplated.

[0026] In some embodiments, the range of suitable tether angles may depend on the overall length of the suspended object. For example, in some embodiments including suspended objects with relatively short overall lengths, tether angles less than or equal to 50 degrees or greater than or equal to 80 degrees may be employed. Alternatively, or in addition, in some embodiments including suspended objects with relatively long overall lengths, tether angles less than or equal to 80 degrees may be employed. Of course, embodiments having other suitable tether angles are also contemplated, depending on the geometry of the suspended object and / or other factors, as appropriate.

[0027] In some instances, the angle for each tether of the multiple tethers is the same, but it should be understood that embodiments in which each tether exhibits a different angle are also contemplated as the disclosure is not limited in this manner, and of course, any suitable combination of angles may be employed depending on the application.

[0028] As described herein, the instantaneous center of rotation of the suspended object may be offset from the bottom surface of the suspended object by a predetermined distance in a direction parallel to the direction of gravity to prevent binding and / or adhesion. Additionally, in some embodiments, the object's instantaneous center of rotation may be positioned such that it is above the suspended object's center of gravity or below the suspended object's bottom surface relative to the center of gravity direction. In some embodiments, the offset may be a percentage of the suspended object's largest dimension parallel to the direction of gravity (e.g., the suspended object's overall length) prior to contact with the stationary object. In some embodiments, the offset distance may be greater than or equal to 50%, 60%, 70%, and / or another suitable percentage of the suspended object's length parallel to the direction of gravity. Correspondingly, the offset distance may be less than or equal to 200%, 100%, 90%, 80%, and / or any other suitable percentage of the suspended object's largest dimension parallel to the direction of gravity. Combinations of the above-listed ranges are also contemplated, including, but not limited to, percentages between or equal to 50% and 200%. Of course, any suitable offset distance percentage for the desired application may be employed, including percentages both smaller and larger than those listed above, depending on the application.

[0029] Assembly devices according to the present disclosure may include any suitable type of flexible tether configured to support an object from a support structure to which the tether is coupled. For example, the flexible tether may be a cable, wire, rope, chain, woven strap, combinations of the foregoing, and / or any other suitable elongated flexible structure capable of suspending an object from a support structure. Thus, as will be understood by one skilled in the art, any suitable type of flexible tether or combination of flexible tether types may be employed depending on the application.

[0030] An assembly apparatus according to the present disclosure may be used in any suitable application. For example, in some embodiments, the assembly apparatus may be attached to or otherwise part of a gantry crane assembly, a crane, or other support structure for placing a first object into a cavity of a second object. Alternatively, or in addition, an assembly apparatus according to the present disclosure may be attached to or otherwise incorporated into an end effector for a robot. Thus, as will be understood by those skilled in the art, an assembly apparatus according to the present disclosure may be used in any suitable application or combination of applications.

[0031] Turning now to the figures, specific, non-limiting embodiments will be described in further detail. It will be understood that the various systems, components, features, and methods described for these embodiments can be used either individually and / or in any desired combination, as the disclosure is not limited to only the specific embodiments described herein.

[0032] FIG. 1 depicts an assembly apparatus 100 for installing a suspended object 102 into a cavity 104 of a stationary object 106, according to one illustrative embodiment. A first object is positioned vertically above the cavity of a second object relative to the direction of gravity G applied to the system and the object. Additionally, a portion of the first object oriented toward the cavity of the second object may be sized and shaped to be received within the cavity once assembled therewith. The assembly apparatus 100 includes a support structure 110 to which two or more flexible tethers 108 are attached. The two flexible tethers 108 are configured to attach to and support the suspended object 102 using any suitable connection to portions of the suspended object on either side of the suspended object's center of gravity such that the suspended object 102 is suspended from the support structure 110 via the flexible tethers 108. Additionally, the support structure 110 may be movable (e.g., up and down) via actuators 112 (e.g., overhead crane) so that the support structure and supported object may be selectively lowered toward the cavity. In the depicted embodiment, the actuators are part of a gantry crane such that the support structure may be moved in one or more horizontal directions relative to the depicted direction of gravity G to properly position the object relative to the cavity to be formed in a second object. Of course, inclusion of the assembly apparatus as part of either another movable structure (e.g., a crane or other system) or a stationary structure is also contemplated.

[0033] In the illustrated embodiment, the assembly apparatus 100 is configured as a passive assembly system. In other words, tension within the flexible tether 108 is maintained solely by gravity, G, and the length of the flexible tether 108 is fixed. Thus, as the actuator 112 moves the support structure 110 upward and / or downward, the suspended object 102 also moves upward and / or downward relative to the underlying second object 106 and cavity 104 formed therein, respectively. In particular, when the suspended object 102 is suspended from the flexible tether 108, the flexible tether 108 is held in a taut state (e.g., under gravity, G) as the support structure 110 is moved upward and / or downward a distance and the suspended object 102 is moved upward and / or downward an equal distance.

[0034] In this manner, assembly apparatus 100 may lower suspended object 102 toward cavity 104 of stationary object 106 while the length and tension of tether 108 are maintained under the influence of gravity G. Stationary object 106, in turn, includes features that may help guide the corresponding portion of suspended object 102 into cavity 104 during insertion. In particular, chamfer 114 may be formed in the second object such that the chamfer, corresponding to an angled surface extending between the upper surface of the object and the inner surface of the cavity, may extend at least partially, and in some cases completely, around the upper opening of cavity 104, where the chamfer is oriented toward the corresponding portion of suspended object 102 and configured to receive it into cavity 104.

[0035] The interaction between the chamfer 114 and the portion of the suspended object 102 contacting the chamfer can help guide the portion of the suspended object into the cavity. For example, FIG. 2A illustrates the suspended object 102 in a position where the lower portion of the suspended object 102 initially contacts the portion of the chamfer 114 that is underlying the portion of the object to be inserted into the cavity. When the suspended object 102 contacts the chamfer 114, the force distribution between the flexible tethers 108 changes, which can change the angle of the associated tether as the orientation of the suspended object changes as the suspended object tilts to one side. At the same time, by appropriately controlling the tether length, angular orientation, and / or force applied across a given object, the portion of the suspended object 102 contacting the chamfer can slide along the chamfer surface toward the cavity 104. In some cases, each tether may remain taut, with a non-zero tension applied to each tether during this initial contact and sliding, in which case the suspended object 102 may function as if connected to the support structure 110 by a rigid link. For example, in the system shown in FIG. 1A , the suspended object may move and rotate as if attached to the support structure by a rigid four-bar link, with the object itself serving as one of the links. However, embodiments in which one or more tethers may be slack, i.e., apply approximately zero tension, are also contemplated. In either case, the suspended object 102 may be guided toward the cavity 104 by the chamfer 114 and flexible tether 108 such that the overall direction of movement of the portion 102 of the suspended object contacting the chamfer is oriented, at least in part, inward toward the cavity 104 of the stationary object 106, which may correspond to the contacting portion of the suspended object sliding along the chamfer surface toward the cavity.

[0036] As described above and illustrated in FIGS. 2A-2C, the suspended object 102 may be placed in a final position within the cavity 104 by sliding along the surface of the chamfer 114 into the cavity 104. In particular, as shown in FIG. 2A, once the suspended object 102 contacts the chamfer 114, the suspended object 102 slides along the chamfer 114 until at least a portion of the suspended object 102 enters the cavity 104. As shown in FIG. 2B, the suspended object 102 may initially contact the interior wall of the cavity 104 at a single point. As the suspended object 102 continues to be lowered into the cavity 104 (e.g., by lowering the support structure 110), the suspended object 102 may then contact the interior wall of the cavity 104 at two points, as shown in FIG. 2C. Once the suspended object 102 contacts the cavity 104 at two points, the reaction force provided by the interior walls of the cavity 104 can serve to provide two points that constrain the orientation and insertion of the portion of the suspended object to be inserted into the cavity. The corresponding portions of the cavity and suspended object may be sized and shaped to allow the object to slide into the cavity without binding after this two-point contact engagement occurs as the suspended object continues to be lowered and confined for insertion. This can allow the suspended object 102 to be positioned in a final desired position within the cavity 104.

[0037] Once the suspended object 102 achieves a two-point contact condition (e.g., as described herein), one of the flexible tethers 108 may relax while the other flexible tether 108 remains tensioned. Thus, a combination of reaction forces from the interior walls of cavity 104 in combination with tension in the remaining tensioned tethers may serve to control the suspended object 102 as it is lowered into cavity 104 until it achieves a desired position within cavity 104. In selected embodiments, tension is maintained in the remaining tensioned tethers due to the force of gravity, G, acting on the tethers.

[0038] Alternatively, or in addition, in some embodiments, the flexible tethers 108 may be actively controlled (e.g., as described in more detail herein). In such embodiments, one or more actuators may actively control the tension in the flexible tethers 108 once the two-point contact condition is achieved, so that the suspended object 102 may move toward a desired orientation. In such embodiments, the tension in the flexible tethers 108 may be controlled together or individually, depending on the application. In some embodiments, the assembly apparatus 100 may include features that enable the assembly apparatus 100 to maintain the suspended object 102 in a generally upright position as it inserts the suspended object 102 into the cavity 104. In particular, the flexible tethers 108 may serve to minimize the angle between the longitudinal axis of the suspended object 102 with respect to the vertical axis A during insertion. For example, as shown in FIG. 2A , the suspended object 102 may be generally aligned with vertical axis A (e.g., because flexible tether 108 is held taut under gravity, G). However, as suspended object 102 slides along chamfer 114, suspended object 102 may be displaced at an angle relative to central axis A by a first angle α1, as shown in FIG. 2B , for example. Additionally, suspended object 102 may be displaced at an angle relative to central axis A by a second angle α2 during final insertion into the cavity. Flexible tether 108 may be configured to orient suspended object 102 such that the angular displacement of suspended object 102 remains below a threshold angle, facilitating both sliding of the object along the chamfer surface and insertion into the cavity without binding, as described above.

[0039] To help avoid binding during insertion of a portion of the object into the cavity, the flexible tether may also serve to maintain the suspended object 102 in an orientation such that the suspended object 102 can fit within the cavity 104 as the suspended object 102 is lowered into the cavity 104. In particular, the flexible tether 108 may hold the suspended object 102 in an orientation such that the horizontal transverse dimension of the suspended object 102 is less than or equal to the horizontal transverse dimension of the opening of the cavity 104 as the suspended object 102 slides along the chamfer 114 and / or enters the opening of the cavity 104 that is oriented toward the suspended object. In particular, in the chamfer-contact position shown in FIG. 2A , the horizontal transverse dimension H1-A of the suspended object 102 is less than or equal to the horizontal transverse dimension H2 of the cavity 104. Relatedly, in the one-point contact position shown in Figure 2B, the horizontal transverse dimension H1-B of suspended object 102 is less than or equal to the horizontal transverse dimension H2 of cavity 104 so that a desired portion of the suspended object can be inserted into the opening of the cavity. Further, in the two-point contact position shown in Figure 2C, the horizontal transverse dimension H1-C of suspended object 102 is less than or equal to the horizontal transverse dimension H2 of cavity 104.

[0040] Although the above considerations are described for a passive system with a tether that is not actively actuated, these concepts for facilitating sliding of a portion of an object contacting a chamfer and final insertion into a cavity are applicable to all of the embodiments described herein. Thus, actively controlled assembly devices can be appropriately controlled to provide the functionality described above as well, as the disclosure is not limited to this format.

[0041] As will be appreciated from the above, the suspended object 102 may rotate (e.g., angularly displace) as it contacts and slides across the surface of the chamfer 114 and reaches its final position within the cavity 104. Such rotation may occur about an instantaneous center of rotation P1, which may be related to the corresponding angle of the flexible tether 108 relative to the suspended object 102; see P1 and P2 in FIGS. 3A-3B . The instantaneous center of rotation may correspond to an imaginary point where lines parallel and coaxial with the tether intersect with each other. Depending on the orientation of the tether, the instantaneous center of rotation may be above, below, or coincident with the bottom surface of the suspended object. In particular, in the configuration depicted in FIG. 3A , lines coaxial with the flexible tether 108 intersect at point P1, which may be located perpendicularly below the bottom surface of the suspended object oriented toward the cavity of another object. Therefore, the suspended object 102 will tend to rotate about point P1. Relatedly, in the configuration shown in Figure 3B, lines coaxial with the flexible tether 108 intersect at point P2. Therefore, the suspended object 102 will tend to rotate about point P2.

[0042] As described above, in some cases, it may be desirable for the tether to be oriented within a particular angular range so that the object's instantaneous center of rotation is offset a predetermined distance from the object's bottom surface to facilitate sliding contact between the object and the corresponding chamfer and insertion of a second object into the cavity. For example, points P1 and P2 may be selected so that the individual suspended objects in each figure can be properly oriented to fit within the corresponding cavity. In particular, suspended object 102 may be oriented to fit within the cavity when points P1, P2 are located outside the object's lower region ab. Thus, pivot points P1, P2 may be positioned above or vertically below the object's lower region ab, as shown in the figures.

[0043] While not wishing to be bound by theory, the location of the instantaneous centers of rotation P1, P2 of the suspended object relative to the depicted region ab may be a function of the angle between the flexible tether 108, the portion of the suspended object to which the tether is connected, and the length of the suspended object 102 relative to a vertical direction parallel to the local direction of gravity G. For example, in the configuration shown in FIG. 3A , the suspended object 102 has a relatively short length L1, and region ab extends along most of length L1. Thus, the angle Θ1 between the flexible tether 108 and a horizontal plane perpendicular to the direction of gravity may be set relatively large (e.g., approximately 90 degrees or another suitable angle, as detailed above) so that the pivot point P1 is outside region ab. Relatedly, in the configuration shown in FIG. 3B , the suspended object 102 has a relatively long length L2 in the vertical direction, and region ab extends along only a small portion of length L2. Therefore, the angle Θ2 between the flexible tether 108 and the horizontal plane can be set to any suitable value such that the pivot point P2 is outside the region ab. In particular, in the embodiment shown in Figure 3B, the angle Θ2 is set relatively small so that the pivot point P2 is vertically above the region ab.

[0044] While the above embodiments show static tether lengths, it should be understood that tethers having lengths and / or angles that are dynamically changed during operation using one or more actuators are also contemplated. Thus, the above discussion related to instantaneous centers of rotation and corresponding relationships may apply to both passively and actively actuated assembly devices, as the disclosure is not so limited.

[0045] Alternatively or additionally to the above, in some embodiments, the assembly apparatus 100 includes features that enable active control of one or more parameters of the flexible tether 108. For example, as shown in FIG. 4 , the assembly apparatus may include one or more actuators 118, depicted as actuated arms configured to actively control the flexible tether 108. In particular, the actuators 118 may be capable of controlling the extension and retraction of the flexible tether 108 relative to a support structure 110 to which the actuators and the tethers are coupled. Thus, the actuators may be used to lower or raise the suspended object 102 relative to the support structure.

[0046] As described above, in some instances, it may be desirable to maintain a predetermined tension applied to multiple tethers used to support an object as it is lowered into a corresponding cavity. Thus, in some embodiments, assembly apparatus 100 may include multiple sensors 116 configured to sense the tension and / or expansion of tethers 108. In the depicted embodiment, the sensors are depicted as being positioned in line with or attached to the tethers. Regardless of the specific organization, the multiple sensors may be operably coupled to a processor 120 configured to control one or more actuators 118 such that the sensors may output one or more sensed parameters to the processor. The processor may be operably coupled with an associated non-transitory processor-readable memory including processor-executable instructions that, when executed by the processor, may implement any of the methods disclosed herein. Processor 120 may control one or more actuators 118 based, at least in part, on one or more parameters sensed by the sensors. The processor 120 may then command the actuators to perform one or more functions on the flexible tethers 108. For example, the actuators may be controlled to maintain tension in each tether above or equal to a predetermined tension while the suspended object 102 is lowered relative to the support structure 110. For example, the tethers may be expanded relative to the support structure while maintaining tension in each of the tethers, or the tethers may be operated to maintain a desired tension in each of the tethers while the support structure is lowered. In either case, the suspended object may be lowered toward the cavity while maintaining tension in each of the tethers during insertion of the object into the cavity. However, embodiments in which one or more of the tethers are allowed to relax during the insertion process are also contemplated, as the disclosure is not so limited.

[0047] FIG. 5 depicts one embodiment of a method that can be implemented to install a first object into a cavity of a second object using an assembly device including a passive motion, in which a tether length can be fixed as the object is lowered toward a cavity of the object that includes a chamfer extending at least partially around the cavity. In FIG. 5 , in step 500, the first object is suspended from a flexible tether of the assembly device in a desired orientation and horizontal position relative to the cavity of the object below the suspended object, such that the portion of the suspended object to be inserted into the cavity is positioned and oriented roughly toward the cavity. Once the object is suspended in the desired orientation and position, in step 502, the object is lowered until it contacts the chamfer of the cavity. Then, in step 504, the flexible tether (e.g., tension) facilitates rotation of the object and sliding of the portion of the suspended first object contacting the chamfer toward the cavity until the object is seated within the cavity. Finally, in step 506, the first object is slid across the surface of the chamfer such that the object makes first contact, followed by second contact, with one or more interior surfaces of the cavity prior to sliding to a desired final position within the cavity. In this passive arrangement, operation of the system may only involve lowering the support structure from which the tether extends, and the overall configuration of the tether and object can help ensure that the object slides properly across various surfaces during insertion without binding, sticking, or moving in undesired directions.

[0048] 6 is a flowchart illustrating an exemplary method for actively controlling the tension applied to a tether of a first suspended object as the first object is inserted into a cavity of a second object positioned vertically below the first object relative to the direction of gravity. Similar to the above embodiment, in step 600, an assembly apparatus can be used to position and orient the first object while it is suspended from the flexible tether toward a corresponding cavity formed in the second object below the first object. Because the present disclosure is not limited to the manner in which the first object is positioned and oriented relative to the second object, this can be done manually and / or the support structure of the apparatus can be moved to the desired position and orientation using one or more corresponding actuators. In either case, one or more actuators of the assembly apparatus can be appropriately controlled in step 602 to extend (i.e., extend the flexible tether) the first object so as to lower it toward the second object. As the first object is lowered, tension in each of the tethers may be sensed at 604 such that a force-based control loop may be implemented to control an actuator associated with the tether. For example, in some embodiments, the actuator may be operated to expand the associated tether so long as the tension sensed in the tether exceeds or equals a predetermined threshold. Correspondingly, expansion of the particular tether may be halted, and in some cases, the tether may be retracted when the sensed tension is below the predetermined threshold. In this manner, tension may be maintained in each of the flexible tethers at 606 as the object is lowered into the cavity. Again, this may help to facilitate sliding of the portion of the first suspended object that contacts the chamfer surrounding the cavity toward the cavity and subsequent insertion of the portion of the first suspended object into the cavity. [Example]

[0049] Example 1: Conditions for successful insertion without relaxation / without adhesion 15A, without wishing to be bound by theory, in the depicted embodiment, the suspended object 102 is held by only two tethers 108. Thus, in the depicted embodiment, neither of the two flexible tethers 108 is relaxed (e.g., by angling the tethers so that they do not fall within region ab, as shown in FIGS. 3A-3B).

[0050] Without wishing to be bound by theory, under such "no relaxation" conditions, the quasi-static motion of the suspended mass 102 may be kinematically determined. Because both flexible tethers 108 are taut, the flexible tethers 108 may be treated as a pair of rigid links. The support structure 100, the two taut flexible tethers 108, and the suspended mass 102 form a four-bar linkage in the vertical plane with only one degree of freedom.

[0051] 7 and 15A illustrate such insertion of suspended object 102 under the "no relaxation" condition described above. As suspended object 102 reaches the surface of chamfer 114, it is constrained by contact with chamfer 114. While not wishing to be bound by theory, the position and orientation of the suspended object may be determined geometrically. As support structure 110 is lowered, the position and orientation of suspended object 102 may vary relative to the height of support structure 110. After reaching the bottom edge of cavity 104, suspended object 102 may contact the edge of cavity 114 on its side, resulting in single point contact with a portion of cavity 104. While not wishing to be bound by theory, in the single point contact condition, the position and orientation of suspended object 102 may be determined kinematically. This continues until the suspended object 102 contacts the interior wall of the cavity 104 at two points, achieving a two-point contact condition. In the two-point contact condition, the suspended object 102 may be constrained on at least two sides of the cavity 104. Once the suspended object 102 is so constrained, the four-bar connection is no longer formed. While not wishing to be bound by theory, in such a condition, at least one flexible tether 108 may relax, satisfying the two-point contact constraint condition. In such a scenario, the unidirectional nature of the tension within the flexible tethers (e.g., the ability of the flexible tether 108 to be tensioned by gravity) releases tension in one or more of the flexible tethers 108 so that the suspended object 102 cannot be over-constrained.

[0052] 7 and 15A, the "no relaxation" condition described above can be maintained throughout the insertion process until two-point contact occurs such that movement of suspended mass 102 can be kinematically controlled as detailed above. By employing appropriate tether angles φ, φ and tether attachment locations such that instantaneous center of rotation P3 can be located away from region ab, suspended mass 102 can be induced through a quasi-static process to reach the two-point contact condition at a sufficient depth within cavity 104 for successful insertion.

[0053] Such a "no relaxation" condition can be satisfied in two ranges of tether orientations: small and large angles. In some cases, adopting an angle in the middle of the range can result in the instantaneous center of rotation P3 falling within region ab, violating the "no relaxation" condition.

[0054] While not wishing to be bound by theory, the selection of the tether angle may depend on the dimensions of the suspended object 102. Figures 3A-3B illustrate two such examples. If the suspended object 102 has a relatively short overall length L1, a larger tether angle Θ1 may be employed, for example, to position the instantaneous center of rotation of the suspended object 102 below region ab. On the other hand, if the suspended object 102 has a relatively long overall length L2, a smaller tether angle Θ2 may be employed, for example, to position the instantaneous center of rotation of the suspended object 102 above region ab.

[0055] Turning to the insertion process, it may be desirable to prevent the suspended object 102 from adhering to the surface of the chamfer 114. To control for this, the inventors first considered the conditions necessary for the suspended object 102 to adhere to the surface of the chamfer 114. This can occur either at the moment when a portion of the suspended object 102 contacts the surface of the chamfer 114, or while the suspended object 102 slides along the chamfer 114. If the suspended object 102 adheres to the surface of the chamfer 114, the suspended object 102 may lose two degrees of freedom. While not wishing to be bound by theory, in such a scenario, the suspended object 102 may rotate only about the point of contact, which may imply that at least one tether becomes loose. Alternatively, if the flexible tether 108 is set with an appropriate angle such that the instantaneous center of rotation P3 does not fall within the region ab, the suspended object 102 cannot adhere to the surface of the chamfer 114 during insertion.

[0056] Using the parameters defined in Figure 7, the no-slack condition for cable angle is given by the following equation: [ka]

[0057] Without wishing to be bound by theory, the above equations can be used to determine two sets of tether angle ranges that can be associated with two scenarios: adhesion on the surface of the chamfer 114 during insertion, and sliding along the surface of the chamfer 114 during insertion. Without wishing to be bound by theory, the static friction coefficient can be used to determine adhesion upon first contact with the chamfer 114, and the kinetic friction coefficient can be used while sliding along the chamfer 114. Similar equations can be derived to determine adhesion conditions during single-point contact.

[0058] However, it should be noted that the "no adhesion" condition described above does not, by itself, guarantee that the suspended object 102 will slide along the chamfer 114. The suspended object 102 may rest on the chamfer surface under certain kinematic conditions. For example, case (B) shown in FIG. 15B illustrates a case where the suspended object 102 may not slide, but instead rests on the chamfer 114.

[0059] In the case (B) configuration of FIG. 15B, the instantaneous center of rotation P3-B is located at the end of the suspended object 102 where the extensions of the two tethers 108 meet. Without wishing to be bound by theory, assume that the left corner of the suspended object 102, i.e., point A in FIG. 7, touches the chamfer. As the suspended object 102 rotates about P3-B, point A is moved upward. If this upward movement is equal to the downward movement of the support structure 110, the two displacements cancel and the suspended object 102 will not slide but will instead rest in a steady state on the chamfer 114. This steady state behavior may be a function of the tether angle, the relative location of the instantaneous center of rotation point A, and / or the chamfer angle α, as shown in FIG. 15A. Additional scenarios were determined for instantaneous center of rotation locations located slightly above the bottom surface of object P3-C in FIG. 15C , located a greater distance above the bottom surface of object P3-D in FIG. 15D , and located below the bottom surface of object P3-E in FIG. 15E . As can be seen in these figures, instantaneous center of rotation locations located a greater distance above and below the bottom surface of the portion of the object to be inserted into the cavity can result in rotation of the portion contacting the chamfer being directed toward the interior of the chamfer where the cavity is located. Thus, the tether of the assembly apparatus may be appropriately configured and / or controlled so that the instantaneous center of rotation of the object can be appropriately positioned to provide sliding movement of the portion of the object contacting the chamfer surface toward the opening of the cavity.

[0060] Without wishing to be bound by theory, if both the "no adhesion" and "no steady state" conditions described above are met, then the suspended object 102 can be expected to slide along the chamfer 114.

[0061] After the suspended object 102 intersects the chamfer 114, the opposite side of the bottom surface of the suspended object 102 (e.g., point B in FIG. 7 ) may overcome the width of the cavity 104 (e.g., H2 in FIGS. 2A-2C ). Without wishing to be bound by theory, a four-bar linkage analysis may be employed to estimate the tilt angle of the suspended object 102 at the point where it reaches the end of the chamfer 114, just before transitioning to a single-point contact condition, as described herein. Without wishing to be bound by theory, as the equation below explains, if the predicted tilt angle of the suspended object 102 satisfies the prescribed constraints, then the opposite side of the bottom surface of the suspended object 102 may be able to overcome the corresponding edge of the cavity 104, as shown in FIG. 7 . [ka]

[0062] The suspended object 102 may then reach a two-point contact state when at least the opposite side of the bottom surface of the suspended object 102 touches the corresponding edge of the cavity 104. Without wishing to be bound by theory, the depth of the first two-point contact location may determine whether the suspended object 102 is attached to the inside of the cavity 104, e.g., whether it becomes wedged within the cavity 104. Wedging may be less likely to occur when the depth of the first two-point contact location is sufficiently deep within the cavity 104. Depending on the given geometry of the suspended object 102, some tether angles may result in a deeper depth of the first two-point contact location than others, making wedging less likely. Such parameters may be selected to ensure that the depth of the first two-point contact location is as deep as possible. Without wishing to be bound by theory, the depth of the first two-point contact location can be determined kinematically and geometrically. (Example 2) Experimental Verification

[0063] Analytical results associated with embodiments of the apparatus and methods disclosed herein were demonstrated through experiments using both 2D and 3D scaling models. For example, as shown in FIG. 8 , a steel peg 126 (0.76 kg) was fabricated to slide into a steel hole 132 with a 45-degree chamfer angle. To avoid nonlinearities associated with sharp edges, a 0.6 mm fillet was implemented on the bottom corner of the peg 126. The peg 126 was connected to a mounting system via low-stretch polyester rope 134, which was attached to a linear guide rail 122 powered by a lead screw. April tags were affixed to the mounting system, peg 126, and hole 132 to provide relative location data for calculations and the angle of the peg's tilt. An indicator LED 128 provided a trigger for when a two-point contact condition was achieved (e.g., as described in more detail herein). Various types of material were placed on the chamfer surface to vary the coefficient of friction for the interaction between the peg and the chamfer (e.g., material 130). The coefficient of friction was measured by placing a piece of material 130 on a steel block and resting the peg 126 on the surface. The angle of the steel block was increased until the peg 126 began to slide along the surface. The angle at which sliding began was measured to be the coefficient of friction angle fs (where m = tan(fs)). In this experiment, the length L of the peg 126 was set to 127 mm, and the width d of the peg 126 was set to 50.8 mm. The chamfer angle α was set to 45 degrees, and the lengths l1 and l2 of the flexible tether 134 were set to 203.2 mm. The diameter D of the hole h was set to 51.82 mm, i.e. the clearance between the peg 126 and the hole was set to 1.02 mm.

[0064] First, an experiment was conducted using three different friction coefficients to verify the success of the chamfer intersection of the peg 126 both when the flexible tether angle was in the acceptable region (e.g., the pivot point was outside region ab, as described above in connection with FIGS. 3A-3B) and when the flexible tether angle was in the unacceptable region (e.g., the pivot point was located within region ab, as described above in connection with FIGS. 3A-3B). As can be seen in FIG. 9, as the coefficient of friction of the peg hole system increases, the range of acceptable initial angles decreases significantly. This experiment verified that the peg 126 would slide within the acceptable region.

[0065] Second, an experiment was conducted in which a simulation of quasi-static chamfer intersection was compared with an actual peg intersecting the chamfer for different initial peg leveling errors. Returning to Figure 7, e values ​​of 1.27 mm, 2.54 mm, and 5.08 mm were tested, representing 2.5%, 5%, and 10% of the experimental peg diameter, respectively. As shown in Figure 10, the data points represent experimentally measured data, and the lines represent predicted values ​​from the simulation. The root mean square error (RMSE) was calculated between the measured and predicted results. For a leveling error e = 1:27 mm, the RMSE was 0.5 degrees; for e = 2:54 mm, the RMSE was 1 degree; and for e = 5:08 mm, the RMSE was 2.4 degrees. This indicates that kinematic analysis can be used to predict the final angle of the peg at the end of the chamfer intersection to within 2.4 degrees over nearly the entire range of flexible tether angles.

[0066] Third, an experiment was conducted in which the depth of first two-point contact (e.g., as part of a trajectory associated with insertion, as described herein) was measured based on different horizontal displacement errors of the peg and different flexible tether mounting angles. The root-mean-square error was calculated between the measured and predicted results. For a horizontal error e = 1:27 mm, the RMSE was 8.9 mm; for e = 2:54 mm, the RMSE was 4.2 mm; and for e = 5:08 mm, the RMSE was 8.6 mm. This indicates that the kinematic model can be trusted to predict the depth of first two-point contact within 7.5% of the peg length for the largest amount of horizontal displacement error that the peg can be expected to experience. As can be seen in Figure 10, the depth l* associated with achieving two-point contact decreases as the flexible tether angle increases. Additionally, as shown in Figure 10, the depth l* increases as the flexible tether angle approaches 90 degrees. This implies that to configure an assembly device for inserting a peg such that the appropriate two-point contact depth l* is achieved, the flexible tether angle can be either as small as possible (e.g., as shown in Figure 3B) or as close to 90 degrees as possible (e.g., as shown in Figure 3A).

[0067] Fourth, additional trials were conducted using a 3D setup as shown in Figure 11, consisting of a 3.5 kg aluminum rounded peg with a diameter of 101.7 mm and a length of 152.4 mm, an aluminum hole with an inner diameter of 101.85 mm, low-stretch polyester rope lengths of 457 mm and 609.6 mm, and a mounting plate with a diameter of 203.2 mm.

[0068] The trial results depicted in FIG. 11 show that over certain cable angles, the peg does not successfully intersect the chamfer and enters the hole. The lines depict travel trajectories where the cable loading angle is inside the predicted, unacceptable region for the particular peg geometry (e.g., region ab as shown in FIGS. 3A-3B). In these cases, the peg may tip forward and tip over. Thus, FIG. 11 shows minimal variation in the peg center-to-hole center distance and the peg depth within the hole within such region. Notably, peg insertion was found to be successful when the flexible tethers were outside this range, specifically when they were loaded at 76 degrees and / or 38 degrees from horizontal. (Example 3) Parameter Examination

[0069] While not wishing to be bound by theory, in some cases, the mechanical behavior of a suspended object, such as a peg, can be determined by applying kinematic principles associated with a four-bar linkage. In particular, the effects of varying the length L of the suspended object 102, the width d of the suspended object 102, and the chamfer angle α were explored. The trajectory of the suspended object 102 with various geometric parameters and various initial cable installation angles was determined, and the instantaneous slope at the first contact point with the chamfer 114 was calculated. If the slope of the instantaneous trajectory contributed to the suspended object 102 sliding along the chamfer, the configuration was deemed acceptable. The results of the parameter exploration are depicted in Figures 12-14.

[0070] The inventors observed that as the length L of the suspended object 102 increases, the region where the pegs will appear in a steady state expands, and the region where sticking may occur transitions toward regions of higher cable angles. Thus, the inventors realized that a smaller cable angle may be associated with successful insertion (e.g., as shown in FIG. 3B ). Additionally, the inventors observed that as the width d of the suspended object 102 increases, the region where sticking may occur expands, while the region where the suspended object 102 may be in a steady state appears to remain approximately the same. The inventors also observed that as the chamfer angle α becomes less steep, the range of valid mounting configurations decreases.

[0071] The above-described embodiments of the techniques described herein can be implemented in any of numerous ways. For example, embodiments may be implemented using hardware, software, or a combination thereof. When implemented in software, the software code can be executed on any suitable processor or collection of processors, whether provided in a single computing device or distributed among multiple computing devices. Such a processor may be implemented as an integrated circuit, with one or more processors within an integrated circuit component, including commercially available integrated circuit components known in the art by names such as CPU chip, GPU chip, microprocessor, microcontroller, or coprocessor. Alternatively, the processor may be implemented within custom circuitry such as an ASIC, semi-custom circuitry resulting from constructing a programmable logic device. Furthermore, as a further alternative, the processor may be part of a larger circuit or semiconductor device, whether commercially available, semi-custom, or custom. As a specific example, some commercially available microprocessors have multiple cores, such that one or a subset of those cores can constitute a processor. However, a processor may be implemented using circuitry in any suitable format.

[0072] The processor may also have one or more input devices and output devices. These devices can be used, among other things, to present a user interface. Examples of output devices that may be used to provide a user interface include a display screen for a visual representation of the output and a speaker or other sound-generating device for an audible representation of the output. Examples of input devices that may be used for a user interface include a keyboard, individual buttons, and pointing devices such as a mouse, touchpad, and digitizing tablet. As another example, a computing device may receive input information through speech recognition or in other audible formats.

[0073] Such processors may be interconnected by one or more networks in any suitable form, including a local area network or a wide area network such as an enterprise network or the Internet. Such networks may be based on any suitable technology and operate according to any suitable protocol, and may include wireless networks, wired networks, or fiber optic networks.

[0074] The various methods or processes outlined herein may also be coded as software that is executable on one or more processors employing any of a variety of operating systems or platforms. In addition, such software may be written using any of a number of suitable programming languages ​​and / or programming or scripting tools, and may be compiled as executable machine language code or intermediate code that runs on a structured or virtual machine.

[0075] In this regard, the embodiments described herein may be embodied as a computer-readable storage medium (or multiple computer-readable media) (e.g., computer memory, one or more floppy disks, compact disks (CDs), optical disks, digital video disks (DVDs), magnetic tape, flash memory, RAM, ROM, EEPROM, circuitry in a field programmable gate array or other semiconductor device, or other tangible computer storage medium) encoded with one or more programs that, when executed on one or more computers or other processors, perform methods that implement the various embodiments discussed above. As is evident from the foregoing examples, a computer-readable storage medium may retain information for a sufficient time to provide computer-executable instructions in a non-transitory form. Such a computer-readable storage medium or media may be transportable, such that the program or programs stored thereon can be loaded onto one or more different computing devices or other processors to implement various aspects of the present disclosure as discussed above. As used herein, the term "computer-readable storage medium" encompasses only non-transitory computer-readable media, which may be considered an article of manufacture (i.e., an article of manufacture) or a machine. Alternatively, or in addition, the present disclosure may be embodied as a computer-readable medium other than a computer-readable storage medium, such as a propagating signal.

[0076] The terms "program" or "software" are used herein in a generic sense to refer to any type of computer code or set of computer-executable instructions that may be employed to program a computing device or other processor to implement various aspects of the present disclosure, as discussed above. Additionally, according to one aspect of the present embodiments, it should be understood that one or more computer programs that, when executed, perform the methods of the present disclosure need not reside on a single computing device or processor, but may be distributed in a modular manner among several different computers or processors to implement various aspects of the present disclosure.

[0077] Computer-executable instructions may be in many forms, such as program modules, executed by one or more computers or other devices. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Typically, the functionality of the program modules may be combined or distributed as desired in various embodiments.

[0078] Various aspects of the present invention may be used alone, in combination, or in various arrangements not specifically discussed in the embodiments described above, and therefore are not limited in their application to the details and arrangements of components set forth in the foregoing description or illustrated in the drawings. For example, aspects described in one embodiment may be combined in any manner with aspects described in other embodiments.

[0079] The embodiments described herein may be embodied as methods, examples of which are provided. The acts performed as part of the method may be ordered in any suitable manner. Thus, although illustrated embodiments show acts as sequential, embodiments may be constructed in which acts are performed in an order different from that shown, which may include performing certain acts simultaneously.

[0080] Additionally, some actions are described as being taken by a "user." It should be understood that a "user" need not be a single individual, and that in some embodiments, actions attributed to a "user" may be performed by a team of individuals and / or individuals in combination with computer-assisted tools or other mechanisms.

[0081] The use of ordinal terms such as "first," "second," "third," etc. in the claims to modify claim elements does not, of itself, imply any priority, precedence, or ordering of one claim element prior to another, or the chronological order in which method actions are performed, but is merely used as a marker to distinguish one claim element having a certain name from another element having the same name (due to the use of ordinal terms) to distinguish between claim elements.

[0082] Also, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of "including," "comprising," "having," "containing," "involving," and variations thereof, as used herein is meant to encompass the items listed thereafter, and equivalents thereof, as well as additional items.

[0083] While the present teachings have been described in conjunction with various embodiments and examples, it is not intended that the present teachings be limited to such embodiments or examples. Rather, the present teachings encompass various alternatives, modifications, and equivalents, as will be appreciated by those skilled in the art. Accordingly, the foregoing description and drawings are by way of example only.

Claims

1. 1. An assembly device comprising: a support structure; a plurality of flexible tethers suspended from the support structure, the plurality of flexible tethers configured to suspend a first object from the support structure; and one or more actuators operably coupled to at least one selected from the group of the support structure and the plurality of flexible tethers, the one or more actuators configured to lower a portion of the first object under the influence of gravity toward a cavity formed in a second object with a chamfer formed along at least a portion of the cavity; Equipped with wherein the one or more actuators and the plurality of flexible tethers are configured to control descent of the portion of the first object such that the portion of the first object contacts and slides along the chamfer as the portion of the first object is inserted into the cavity, and the one or more actuators are configured to control a length of at least one flexible tether of the plurality of flexible tethers.

2. 2. The assembly apparatus of claim 1, wherein the one or more actuators are configured to maintain a predetermined tension within each flexible tether of the plurality of flexible tethers as the portion of the first object is lowered into the cavity.

3. The assembly apparatus of claim 1 , wherein the one or more actuators are configured to lower the support structure.

4. The assembly apparatus of claim 3 , wherein the one or more actuators include a plurality of actuators configured to expand the plurality of flexible tethers and lower the first object.

5. The assembly apparatus of claim 4 , wherein the plurality of flexible tethers includes one or more sensors configured to sense tension in the plurality of flexible tethers.

6. 6. The assembly apparatus of claim 5, wherein the one or more actuators are configured to modify tension in the plurality of flexible tethers based at least in part on the sensed tension.

7. The assembly device of claim 6 , wherein the one or more actuators are configured to be controlled by a processor based at least in part on the sensed tension.

8. 2. The assembly apparatus of claim 1, wherein the one or more actuators and the plurality of flexible tethers are configured to maintain the first object in a substantially upright position while the first object is lowered into the cavity of the second object.

9. The assembly apparatus of claim 1 , wherein the plurality of flexible tethers includes two flexible tethers configured to move the first object in two dimensions.

10. The assembly apparatus of claim 1 , wherein the plurality of flexible tethers comprises three flexible tethers configured to move the first object in three dimensions.

11. 2. The assembly apparatus of claim 1, wherein the one or more actuators are configured to move the first object such that a magnitude of movement of the portion of the first object toward the cavity of the second object exceeds a magnitude of movement of the portion of the first object away from the cavity of the second object as the first object slides along the chamfer of the second object.

12. 2. The assembly apparatus of claim 1, wherein lines extending coaxially with the plurality of flexible tethers intersect at an intersection point that is offset a predetermined distance in a vertical direction from a bottom surface of the portion of the first object that is oriented toward the cavity, the vertical direction being parallel to the direction of gravity.

13. 13. The assembly apparatus of claim 12, wherein the predetermined distance is offset from the bottom surface by at least 50% of an overall length of the first object, the overall length being parallel to a direction of gravity.

14. 13. The assembly apparatus of claim 12, further comprising a processor configured to control the one or more actuators such that a length of each flexible tether of the plurality of flexible tethers is set such that the intersection is offset from the bottom surface by at least the predetermined distance.

15. 1. A method of placing an object in a cavity, comprising: suspending a first object from a plurality of flexible tethers of an assembly apparatus; using one or more actuators to control a length of at least one flexible tether of the plurality of flexible tethers; lowering a portion of the first object under the influence of gravity toward a cavity formed in a second object with the chamfer formed along at least a portion of the cavity such that at least a portion of the first object contacts the chamfer; sliding the portion of the first object along the chamfer; placing the first object within the cavity of the second object; A method comprising:

16. The method of claim 15 , wherein lowering the first object into the cavity of the second object comprises lowering the plurality of flexible tethers.

17. 17. The method of claim 16, wherein lowering the plurality of flexible tethers comprises maintaining a predetermined tension within each flexible tether of the plurality of flexible tethers as the portion of the first object is lowered into the cavity of the second object.

18. The method of claim 15 , wherein lowering the first object into the cavity includes maintaining the first object in a generally upright position.

19. 16. The method of claim 15, wherein sliding the portion of the first object along the chamfer comprises moving the first object such that a magnitude of movement of the portion of the first object toward the cavity of the second object exceeds a magnitude of movement of the portion of the first object away from the cavity of the second object.

20. 16. The method of claim 15, wherein suspending the first object from the plurality of flexible tethers of the assembly apparatus comprises suspending the first object so that lines extending coaxially with the plurality of flexible tethers intersect at an intersection point, the intersection point being offset a predetermined distance in a vertical direction from a bottom surface of the portion of the first object oriented toward the cavity, the vertical direction being parallel to the direction of gravity.

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