Position forward and inverse solution method of three-axis parallel mechanism and three-axis parallel mechanism

Abstract

The present application relates to a kind of three-axis parallel mechanism position forward and inverse solution method and three-axis parallel mechanism.The three-axis parallel mechanism of the present application, first three-axis parallel mechanism includes movable platform;First T-shaped rod, first swing arm, first connecting rod, first linear feed device form first kinematic chain, the first linear feed device is formed by first slider and first guide rail;Second T-shaped rod, second swing arm, second connecting rod, second linear feed device form second kinematic chain, the second linear feed device is formed by second slider and second guide rail;Third T-shaped rod, third swing arm, third connecting rod, third linear feed device form third kinematic chain, the third linear feed device is formed by third slider and third guide rail;The first kinematic chain, second kinematic chain and third kinematic chain structure are same.The method is a kind of numerical solution method in combination with robotics theory, the present application has higher solution accuracy.

Description

Technical Field

[0001] This invention relates to the field of robotics, and in particular to a method for forward and inverse kinematics of a three-axis parallel mechanism and the three-axis parallel mechanism itself. Background Technology

[0002] Currently, triaxial parallel mechanisms with two rotational degrees of freedom and one translational degree of freedom are a very important type of parallel mechanism with few degrees of freedom. These parallel mechanisms have advantages such as a high stiffness-to-mass ratio, high load capacity, and compact structure, which can effectively save costs in system design, manufacturing, and control in practical engineering applications.

[0003] The most common spatial parallel mechanism with one translational and two rotational components consists of a stationary platform, a moving platform, and three identical branches. In this type of parallel mechanism, the branches are evenly distributed circumferentially in space, the end effector is fixedly connected to the moving platform, and the guide rails are parallel to the direction of rotation. z In the feed direction. In a parallel mechanism with this structural form, each branch can move independently in a straight line under the drive of the feed device, such as a combination of a servo motor and a lead screw and nut pair, thereby causing the moving platform to move relative to the fixed frame along the axis of symmetry and rotate about two orthogonal axes perpendicular to that axis.

[0004] To develop a control system for novel parallel mechanisms and achieve precise motion control, ultimately enabling high-precision machining, the forward and inverse kinematics algorithms for parallel mechanisms are the primary issues that need to be addressed. These algorithms can be used for workspace analysis, end-effector trajectory analysis, component structural design, and standard part selection before robot manufacturing. They are also a crucial element in ensuring high-precision machining along a specified end-effector trajectory.

[0005] However, existing commercial simulation software is closed-source software, which means that designers can only obtain its calculation results but cannot gain an in-depth understanding of the operating principle of parallel mechanisms, thus limiting the design and motion control of mechanisms. Summary of the Invention

[0006] The technical problem solved by this invention is to provide a method for forward and inverse solving of the position of a three-axis parallel mechanism and a three-axis parallel mechanism.

[0007] In a first aspect, the present invention provides a three-axis parallel mechanism, the first three-axis parallel mechanism including a moving platform; a first T-shaped rod, a first swing arm, a first connecting rod, and a first linear feed device forming a first motion branch, the first linear feed device being composed of a first slider and a first guide rail; a second T-shaped rod, a second swing arm, a second connecting rod, and a second linear feed device forming a second motion branch, the second linear feed device being composed of a second slider and a second guide rail; a third T-shaped rod, a third swing arm, a third connecting rod, and a third linear feed device forming a third motion branch, the third linear feed device being composed of a third slider and a third guide rail; the first motion branch, the second motion branch, and the third motion branch have the same structure.

[0008] One end of the moving platform is connected to one end of a first T-shaped rod (second T-shaped rod / third T-shaped rod) via a hinge with one degree of rotational freedom; the other end of the first T-shaped rod (second T-shaped rod / third T-shaped rod) is connected to one end of a first swing arm (second swing arm / third swing arm) via a hinge with one degree of rotational freedom; the other end of the first swing arm (second swing arm / third swing arm) is connected to one end of a first connecting rod (second connecting rod / third connecting rod) via a hinge with one degree of rotational freedom; the other end of the first connecting rod (second connecting rod / third connecting rod) is connected to a first slider (second slider / third slider) via a hinge with one degree of rotational freedom; the first slider (second slider / third slider) is connected to a first guide rail (second guide rail / third guide rail) via a single-degree-of-freedom moving joint; the first guide rail (second guide rail / third guide rail) is fixedly connected to the static platform.

[0009] The rotation axis connecting the first slider (second slider / third slider) and the first connecting rod (second connecting rod / third connecting rod) is perpendicular to and intersects the axis of the sliding joint connecting the first slider (second slider / third slider) and the first guide rail (second guide rail / third guide rail); and is perpendicular to and intersects the direction vector along the first connecting rod (second connecting rod / third connecting rod); and is perpendicular to but does not intersect the rotation axis connecting the first swing arm (second swing arm / third swing arm) and the first connecting rod (second connecting rod / third connecting rod); the axis connecting the first swing arm (second swing arm / third swing arm) and the first connecting rod (second connecting rod / third connecting rod) is perpendicular to but does not intersect the rotation axis of the first swing arm (second swing arm / third swing arm). The rotation axis of the first swing arm (second swing arm / third swing arm) and the first T-shaped rod (second T-shaped rod / third T-shaped rod) is perpendicular to and intersects the rotation axis of the first swing arm (second swing arm / third swing arm) and the first T-shaped rod (second T-shaped rod / third T-shaped rod); and is perpendicular to and intersects the direction vector along the first link (second link / third link); the rotation axis of the first swing arm (second swing arm / third swing arm) and the first T-shaped rod (second T-shaped rod / third T-shaped rod) is perpendicular to and intersects the rotation axis of the moving platform and the first T-shaped rod (second T-shaped rod / third T-shaped rod).

[0010] The second three-axis parallel mechanism includes a moving platform; a first motion branch consisting of a first swing arm, a first T-shaped rod, a first connecting rod, and a first linear feed device, the first linear feed device consisting of a first slider and a first guide rail; a second motion branch consisting of a second swing arm, a second T-shaped rod, a second connecting rod, and a second linear feed device, the second linear feed device consisting of a second slider and a second guide rail; and a third motion branch consisting of a third swing arm, a third T-shaped rod, a third connecting rod, and a third linear feed device, the third linear feed device consisting of a third slider and a third guide rail; the first, second, and third motion branches have the same structure.

[0011] One end of the moving platform is connected to one end of the first swing arm (second swing arm / third swing arm) via a hinge with one degree of rotational freedom; the other end of the first swing arm (second swing arm / third swing arm) is connected to one end of the first T-shaped rod (second T-shaped rod / third T-shaped rod) via a hinge with one degree of rotational freedom; the other end of the first T-shaped rod (second T-shaped rod / third T-shaped rod) is connected to one end of the first connecting rod (second connecting rod / third connecting rod) via a hinge with one degree of rotational freedom; the other end of the first connecting rod (second connecting rod / third connecting rod) is connected to the first slider (second slider / third slider) via a hinge with one degree of rotational freedom; the first slider (second slider / third slider) is connected to the first guide rail (second guide rail / third guide rail) via a single-degree-of-freedom moving joint; the first guide rail (second guide rail / third guide rail) is fixedly connected to the static platform.

[0012] The rotation axis connecting the first slider (second slider / third slider) and the first connecting rod (second connecting rod / third connecting rod) is perpendicular to and intersects the axis of the sliding joint connecting the first slider (second slider / third slider) and the first guide rail (second guide rail / third guide rail); and is perpendicular to and intersects the direction vector along the first connecting rod (second connecting rod / third connecting rod); the rotation axis connecting the first T-shaped rod (second T-shaped rod / third T-shaped rod) and the first swing arm (second swing arm / third swing arm) is perpendicular to and intersects the direction vector along the first connecting rod (second connecting rod / third connecting rod); and is perpendicular to and intersects the direction vector along the first swing arm (second swing arm / third swing arm); and is perpendicular to but does not intersect the rotation axis connecting the moving platform and the first swing arm (second swing arm / third swing arm); the rotation axis connecting the moving platform and the first swing arm (second swing arm / third swing arm) is perpendicular to and intersects the direction vector along the first swing arm (second swing arm / third swing arm).

[0013] A method for forward and inverse kinematics of a three-axis parallel mechanism includes the following steps: S1: Establish the forward and inverse kinematics model based on the first three-axis parallel mechanism, at the origin of the static platform. Establish a base coordinate system at the reference point at the end of the moving platform. A local connected coordinate system is established. The initial positions of the first, second, and third guide rails are: The intersection points of the sliding joint axis connecting the first slider and the first guide rail with the rotation axis connecting the first connecting rod and the first slider, the intersection points of the sliding joint axis connecting the second slider and the second guide rail with the rotation axis connecting the second connecting rod and the second slider, and the intersection points of the sliding joint axis connecting the third slider and the third guide rail with the rotation axis connecting the third connecting rod and the third slider are: The points where the rotation axis connecting the first link and the first swing arm intersects with the direction vector along the first swing arm, the points where the rotation axis connecting the second link and the second swing arm intersects with the direction vector along the second swing arm, and the points where the rotation axis connecting the third link and the third swing arm intersects with the direction vector along the third swing arm are: The points where the rotation axis connecting the moving platform and the first T-shaped rod intersects with the direction vector along the first swing arm, the points where the rotation axis connecting the moving platform and the second T-shaped rod intersects with the direction vector along the second swing arm, and the points where the rotation axis connecting the moving platform and the third T-shaped rod intersects with the direction vector along the third swing arm are: .

[0014] S2: Obtain the attitude matrix of the moving platform relative to the base coordinate system. End reference point Position vector in the base coordinate system The virtual circumcircle radius of the static platform The radius of the virtual circumscribed circle of the moving platform and branch offset angle .

[0015] S3: By using the aforementioned branch offset angle and coordinate transformation, the coordinates in the local reference frame are obtained. coordinates By and the attitude matrix Multiply and then sum Add them together to obtain the coordinates in the base coordinate system. coordinate.

[0016] S4: According to the above coordinates and Coordinates can be used to obtain vectors. , The length of the first connecting rod (113) after taking the mold is always the same. Therefore, the first set of constraint equations can be obtained:

[0017] S5: According to the above coordinates and Coordinates can be used to obtain vectors. , The length of the first swing arm (112) after taking the mold is always the same. Therefore, the second set of constraint equations can be obtained:

[0018] S6: According to the above Coordinates can be used to obtain vectors ,in , and According to the above with vector Since they are perpendicular to each other, their dot product is zero. Therefore, we can derive the third set of constraint equations:

[0019] S7: According to the above Coordinates can be used to obtain vectors ,in , and According to the above with vector Since they are perpendicular to each other, their dot product is zero. Therefore, we can derive the fourth set of constraint equations:

[0020] S8: Based on the rotation axis connecting the first link and the first swing arm, the rotation axis of the second link and the second swing arm, the rotation axis of the third link and the third swing arm, and the vector... Since they are perpendicular to each other, their dot product is zero. Therefore, we can derive the fifth set of constraint equations:

[0021] S9: Establish the forward and inverse kinematics model based on the second three-axis parallel mechanism, and redefine the intersection points of the rotation axes connecting the first swing arm and the first T-shaped rod with the direction vector along the first connecting rod, the intersection points of the rotation axes of the second swing arm and the second T-shaped rod with the direction vector along the second connecting rod, and the intersection points of the rotation axes of the third swing arm and the third T-shaped rod with the direction vector along the third connecting rod. The intersection points of the rotation axes connecting the moving platform and the first swing arm with the direction vector along the first swing arm, the intersection points of the rotation axes connecting the moving platform and the second swing arm with the direction vector along the second swing arm, and the intersection points of the rotation axes connecting the moving platform and the third swing arm with the direction vector along the third swing arm are redefined as follows: The process of establishing the first, second, third, and fourth constraint equation sets of the second three-axis parallel mechanism is consistent with steps S1, S2, S3, S4, S5, S6, and S7.

[0022] S10: Based on the rotation axes of the first swing arm and the first T-shaped rod, the rotation axes of the second swing arm and the second T-shaped rod, and the rotation axes of the third swing arm and the third T-shaped rod, and the vector... Since they are perpendicular to each other, their dot product is zero. Therefore, we can derive the sixth set of constraint equations:

[0023] S11: Based on the meaning of inverse kinematics, given the end trajectory of the moving platform, by simultaneously solving the first, second, third, fourth, and fifth constraint equations, the position coordinates of the first parallel mechanism can be solved. Given the end trajectory of the moving platform, by simultaneously solving the first, second, third, fourth, and sixth constraint equations, the position coordinates of the second parallel mechanism can be determined. Based on the meaning of the correct kinematic solution, given the above... By simultaneously solving the first, second, third, fourth, and fifth constraint equations, the terminal trajectory of the moving platform can be obtained.

[0024] The above method further includes the following steps: receiving the motion command of the three-axis parallel mechanism, the motion command including at least one of the following: translation, rotation; outputting a trajectory sequence according to the motion command; outputting a motion command according to the trajectory sequence; and setting the... The position vector is output to the motor servo system, enabling the motor servo system to control the three-axis parallel mechanism to complete the target motion trajectory; the end trajectory is output to the host computer system, enabling the host computer to obtain the end reference point pose of the three-axis parallel mechanism to complete motion control. The iterative method includes, but is not limited to, the Newton-Raphson numerical method.

[0025] Secondly, the present invention provides a three-axis parallel mechanism, comprising: at least one memory and at least one processor; the memory and at least one processor; when the one or more programs are executed by the at least one processor, the at least one processor implements the steps of the position forward and inverse kinematics method of the three-axis parallel mechanism as described in the first aspect of the present invention. The linear feed system in the three-axis parallel mechanism includes the following linear drive forms: a motor screw, a pneumatic or hydraulic device.

[0026] The advantages and positive effects of this invention are: 1. The branches of the three-axis parallel mechanism are evenly distributed circumferentially in space, which, compared to serial robots, results in a higher stiffness-to-mass ratio and stronger load capacity. The three-axis parallel mechanism has a compact structure and small size, and can be used as a plug-and-play power module, further meeting the needs of integrated design and manufacturing.

[0027] 2. The forward and inverse kinematics algorithms can be used for workspace analysis, end-effector trajectory analysis, component structural design, and standard part selection before robot manufacturing. They are also an important part of enabling parallel mechanisms to perform high-precision machining along a specified end-effector trajectory through the control system. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the structure of the first three-axis parallel mechanism; Figure 2 This is a schematic diagram of the second and third axis parallel mechanism; Figure 3 This is a schematic diagram of the coordinate system and reference points of the first three-axis parallel mechanism; Figure 4 This is a schematic diagram of the coordinate system and reference points of the second and third axis parallel mechanism; Figure 5 This is a schematic diagram of the branch structure of the first three-axis parallel mechanism; Figure 6 This is a schematic diagram of the branch structure of the second and third axis parallel mechanism; Figure 7 This is a schematic diagram of the structure of an embodiment of the invention; Figure 8 This is a schematic diagram of the second embodiment of the invention. Detailed Implementation

[0029] The forward and inverse kinematics methods and the three-axis parallel mechanism are described in detail below with reference to the accompanying drawings and embodiments.

[0030] like Figure 1-8 As shown, the first three-axis parallel mechanism includes a moving platform 1; a first T-shaped rod 111, a first swing arm 112, a first connecting rod 113, and a first linear feed device form a first motion branch, the first linear feed device being composed of a first slider 114 and a first guide rail 115; a second T-shaped rod 121, a second swing arm 122, a second connecting rod 123, and a second linear feed device form a second motion branch, the second linear feed device being composed of a second slider 124 and a second guide rail 125; a third T-shaped rod 131, a third swing arm 132, a third connecting rod 133, and a third linear feed device form a third motion branch, the third linear feed device being composed of a third slider 134 and a third guide rail 135; the first motion branch, the second motion branch, and the third motion branch have the same structure.

[0031] One end of the moving platform 1 is connected to one end of the first T-shaped rod 111 (second T-shaped rod 121 / third T-shaped rod 131) via a hinge with one degree of rotational freedom; the other end of the first T-shaped rod 111 (second T-shaped rod 121 / third T-shaped rod 131) is connected to one end of the first swing arm 112 (second swing arm 122 / third swing arm 132) via a hinge with one degree of rotational freedom; the other end of the first swing arm 112 (second swing arm 122 / third swing arm 132) is connected to one end of the first connecting rod 113 (first T-shaped rod 131) via a hinge with one degree of rotational freedom. One end of the first link 113 (second link 123 / third link 133) is connected; the other end of the first link 113 (second link 123 / third link 133) is connected to the first slider 114 (second slider 124 / third slider 134) through a hinge with one degree of rotational freedom; the first slider 114 (second slider 124 / third slider 134) is connected to the first guide rail 115 (second guide rail 125 / third guide rail 135) through a single degree of freedom moving joint; the first guide rail 115 (second guide rail 125 / third guide rail 135) is fixedly connected to the static platform.

[0032] The rotation axis connecting the first slider 114 (second slider 124 / third slider 134) and the first connecting rod 113 (second connecting rod 123 / third connecting rod 133) is perpendicular to and intersects the axis of the sliding joint connecting the first slider 114 (second slider 124 / third slider 134) and the first guide rail 115 (second guide rail 125 / third guide rail 135); and is perpendicular to and intersects the vector along the direction of the first connecting rod 113 (second connecting rod 123 / third connecting rod 133); and is perpendicular to but does not intersect the rotation axis connecting the first swing arm 112 (second swing arm 122 / third swing arm 132) and the first connecting rod 113 (second connecting rod 123 / third connecting rod 133); The rotation axis of the swing arm 132 and the first connecting rod 113 (second connecting rod 123 / third connecting rod 133) is perpendicular to and intersects the rotation axis connecting the first swing arm 112 (second swing arm 122 / third swing arm 132) and the first T-shaped rod 111 (second T-shaped rod 121 / third T-shaped rod 131); and is perpendicular to and intersects the direction vector along the first connecting rod 113 (second connecting rod 123 / third connecting rod 133); the rotation axis connecting the first swing arm 112 (second swing arm 122 / third swing arm 132) and the first T-shaped rod 111 (second T-shaped rod 121 / third T-shaped rod 131) is perpendicular to and intersects the rotation axis connecting the moving platform 1 and the first T-shaped rod 111 (second T-shaped rod 121 / third T-shaped rod 131).

[0033] The second three-axis parallel mechanism includes a moving platform 2; a first motion branch consisting of a first swing arm 211, a first T-shaped rod 212, a first connecting rod 213, and a first linear feed device, wherein the first linear feed device consists of a first slider 214 and a first guide rail 215; a second motion branch consisting of a second swing arm 221, a second T-shaped rod 222, a second connecting rod 223, and a second linear feed device, wherein the second linear feed device consists of a second slider 224 and a second guide rail 225; a third motion branch consisting of a third swing arm 231, a third T-shaped rod 232, a third connecting rod 233, and a third linear feed device, wherein the third linear feed device consists of a third slider 234 and a third guide rail 235; the first, second, and third motion branches have the same structure.

[0034] One end of the moving platform 2 is connected to one end of the first swing arm 211 (second swing arm 221 / third swing arm 231) via a hinge with one degree of rotational freedom; the other end of the first swing arm 211 (second swing arm 221 / third swing arm 231) is connected to one end of the first T-shaped rod 212 (second T-shaped rod 222 / third T-shaped rod 232) via a hinge with one degree of rotational freedom; the other end of the first T-shaped rod 212 (second T-shaped rod 222 / third T-shaped rod 232) is connected to the first connecting rod 213 (first T-shaped rod 232) via a hinge with one degree of rotational freedom. One end of the first link 213 (second link 223 / third link 233) is connected to the first slider 214 (second slider 224 / third slider 234) via a hinge with one degree of rotational freedom; the first slider 214 (second slider 224 / third slider 234) is connected to the first guide rail 215 (second guide rail 225 / third guide rail 235) via a single-degree-of-freedom moving joint; the first guide rail 215 (second guide rail 225 / third guide rail 235) is fixedly connected to the static platform.

[0035] The rotation axis connecting the first slider 214 (second slider 224 / third slider 234) and the first connecting rod 213 (second connecting rod 223 / third connecting rod 233) is perpendicular to and intersects the axis of the sliding joint connecting the first slider 214 (second slider 224 / third slider 234) and the first guide rail 215 (second guide rail 225 / third guide rail 235); and is perpendicular to and intersects the direction vector along the first connecting rod 213 (second connecting rod 223 / third connecting rod 233); the axis connecting the first T-shaped rod 212 (second T-shaped rod 222 / third T-shaped rod 232) and the first swing arm 211 (second swing arm 221 / third T-shaped rod 232) is perpendicular to and intersects the axis of the sliding joint connecting the first slider 214 (second slider 224 / third slider 234) and the first guide rail 215 (second guide rail 225 / third guide rail 235). The rotation axis of the three swing arms 231 is perpendicular to and intersects the direction vector along the first link 213 (second link 223 / third link 233); and is perpendicular to and intersects the direction vector along the first swing arm 211 (second swing arm 221 / third swing arm 231); and is perpendicular to and does not intersect the rotation axis connecting the moving platform 2 and the first swing arm 211 (second swing arm 221 / third swing arm 231); the rotation axis connecting the moving platform 2 and the first swing arm 211 (second swing arm 221 / third swing arm 231) is perpendicular to and intersects the direction vector along the first swing arm 211 (second swing arm 221 / third swing arm 231).

[0036] In view of the three-axis parallel mechanism described in the above embodiments, the present invention also provides a method for forward and inverse kinematics of the position of the three-axis parallel mechanism, which is described in detail below: S1: Establish the forward and inverse kinematics model based on the first three-axis parallel mechanism, at the origin of the static platform. Establish a base coordinate system at the reference point at the end of the moving platform 1. A local coordinate system is established. The initial positions of the first guide rail 115, the second guide rail 125, and the third guide rail 135 are: The intersection points of the sliding joint axis connecting the first slider 114 and the first guide rail 115 with the rotation axis connecting the first connecting rod 113 and the first slider 114, the intersection points of the sliding joint axis connecting the second slider 124 and the second guide rail 125 with the rotation axis connecting the second connecting rod 123 and the second slider 124, and the intersection points of the sliding joint axis connecting the third slider 134 and the third guide rail 135 with the rotation axis connecting the third connecting rod 133 and the third slider 134 are: The points where the rotation axis connecting the first link 113 and the first swing arm 112 intersects with the direction vector along the first swing arm 112, the points where the rotation axis connecting the second link 123 and the second swing arm 122 intersects with the direction vector along the second swing arm 122, and the points where the rotation axis connecting the third link 133 and the third swing arm 132 intersects with the direction vector along the third swing arm 132 are: The points where the rotation axis connecting the moving platform 1 and the first T-shaped rod 111 intersects with the direction vector along the first swing arm 112, the points where the rotation axis connecting the moving platform 1 and the second T-shaped rod 121 intersects with the direction vector along the second swing arm 122, and the points where the rotation axis connecting the moving platform 1 and the third T-shaped rod 131 intersects with the direction vector along the third swing arm 132 are: .

[0037] S2: Obtain the attitude matrix of the moving platform 1 relative to the base coordinate system. End reference point Position vector in the base coordinate system The virtual circumcircle radius of the static platform The radius of the virtual circumscribed circle of the moving platform 1 and branch offset angle .

[0038] S3: By using the aforementioned branch offset angle and coordinate transformation, the coordinates in the local reference frame are obtained. coordinates By and the attitude matrix Multiply and then sum Add them together to obtain the coordinates in the base coordinate system. coordinate.

[0039] S4: According to the above coordinates and Coordinates can be used to obtain vectors. , The length of the first connecting rod (113) after taking the mold is always the same. Therefore, the first set of constraint equations can be obtained:

[0040] S5: According to the above coordinates and Coordinates can be used to obtain vectors. , The length of the first swing arm (112) after taking the mold is always the same. Therefore, the second set of constraint equations can be obtained:

[0041] S6: According to the above Coordinates can be used to obtain vectors ,in , and According to the above with vector Since they are perpendicular to each other, their dot product is zero. Therefore, we can derive the third set of constraint equations:

[0042] S7: According to the above Coordinates can be used to obtain vectors ,in , and According to the above with vector Since they are perpendicular to each other, their dot product is zero. Therefore, we can derive the fourth set of constraint equations:

[0043] S8: Based on the rotation axis connecting the first link 113 and the first swing arm 112, the rotation axis of the second link 123 and the second swing arm 122, the rotation axis of the third link 133 and the third swing arm 132, and the vector... Since they are perpendicular to each other, their dot product is zero. Therefore, we can derive the fifth set of constraint equations:

[0044] S9: Establish the forward and inverse kinematics model based on the second three-axis parallel mechanism, and redefine the intersection points of the rotation axes connecting the first swing arm 211 and the first T-shaped rod 212 with the direction vector along the first connecting rod 213, the intersection points of the rotation axes of the second swing arm 221 and the second T-shaped rod 222 with the direction vector along the second connecting rod 223, and the intersection points of the rotation axes of the third swing arm 231 and the third T-shaped rod 232 with the direction vector along the third connecting rod 233. The intersection points of the rotation axis connecting the moving platform 2 and the first swing arm 211 with the direction vector along the first swing arm 211, the intersection points of the rotation axis connecting the moving platform 2 and the second swing arm 221 with the direction vector along the second swing arm 221, and the intersection points of the rotation axis connecting the moving platform 2 and the third swing arm 231 with the direction vector along the third swing arm 231 are redefined as follows: The process of establishing the first, second, third, and fourth constraint equation sets of the second three-axis parallel mechanism is consistent with steps S1, S2, S3, S4, S5, S6, and S7.

[0045] S10: Based on the rotation axes of the first swing arm 211 and the first T-shaped rod 212, the rotation axes of the second swing arm 221 and the second T-shaped rod 222, the rotation axes of the third swing arm 231 and the third T-shaped rod 232, and the vector... Since they are perpendicular to each other, their dot product is zero. Therefore, we can derive the sixth set of constraint equations:

[0046] S11: Based on the meaning of inverse kinematics, given the end trajectory of the moving platform 1, by simultaneously solving the first, second, third, fourth, and fifth constraint equations, the position coordinates of the first parallel mechanism can be solved. Given the end trajectory of the moving platform 2, by simultaneously solving the first, second, third, fourth, and sixth constraint equations, the position coordinates of the second parallel mechanism can be determined. Based on the meaning of the correct kinematic solution, given the above... By solving the first, second, third, fourth, and fifth constraint equations simultaneously, the terminal trajectory of moving platform 1 can be obtained; by solving the first, second, third, fourth, and sixth constraint equations simultaneously, the terminal trajectory of moving platform 2 can be obtained.

[0047] Example: An operator manipulates the three-axis parallel mechanism through a control system. The software of the control system includes the position forward and inverse kinematics algorithm of this invention. The steps include: receiving motion commands from the three-axis parallel mechanism, which include at least one of the following: translation or rotation; outputting a trajectory sequence based on the motion commands; outputting motion commands based on the trajectory sequence; outputting the position vector of the linear feed device to the motor servo system, enabling the motor servo system to control the three-axis parallel mechanism to complete the target motion trajectory; outputting the end-effector trajectory to the host computer system, allowing the host computer to obtain the end-effector reference point pose of the three-axis parallel mechanism to complete motion control. Ultimately, the three-axis parallel mechanism is controlled to complete machining. Figure 7 and Figure 8 As shown, the three-axis parallel mechanism can form a parallel power head with the static platform, serving as a plug-and-play machining module that can further meet the needs of integrated machining.

[0048] Although the embodiments of the present invention have been described above, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims, and these all fall within the scope of protection of the present invention.

Claims

1. A three-axis parallel mechanism, characterized in that: The first three-axis parallel mechanism includes a moving platform (1); a first T-shaped rod (111), a first swing arm (112), a first connecting rod (113), and a first linear feed device form a first motion branch, the first linear feed device being composed of a first slider (114) and a first guide rail (115); a second T-shaped rod (121), a second swing arm (122), a second connecting rod (123), and a second linear feed device form a second motion branch, the second linear feed device being composed of a second slider (124) and a second guide rail (125); a third T-shaped rod (131), a third swing arm (132), a third connecting rod (133), and a third linear feed device form a third motion branch, the third linear feed device being composed of a third slider (134) and a third guide rail (135); the first motion branch, the second motion branch, and the third motion branch have the same structure; One end of the moving platform (1) is connected to one end of the first T-shaped rod (111) via a hinge with one degree of rotational freedom; the other end of the first T-shaped rod (111) is connected to one end of the first swing arm (112) via a hinge with one degree of rotational freedom; the other end of the first swing arm (112) is connected to one end of the first connecting rod (113) via a hinge with one degree of rotational freedom; the other end of the first connecting rod (113) is connected to the first slider (114) via a hinge with one degree of rotational freedom; the first slider (114) is connected to the first guide rail (115) via a single-degree-of-freedom moving joint; the first guide rail (115) is fixedly connected to the static platform; The rotation axis connecting the first slider (114) and the first connecting rod (113) is perpendicular to and intersects the axis of the sliding joint connecting the first slider (114) and the first guide rail (115); and is perpendicular to and intersects the vector along the direction of the first connecting rod (113); and is perpendicular to but does not intersect the rotation axis connecting the first swing arm (112) and the first connecting rod (113); the rotation axis connecting the first swing arm (112) and the first connecting rod (113) is perpendicular to and intersects the rotation axis connecting the first swing arm (112) and the first T-shaped rod (111); and is perpendicular to and intersects the vector along the direction of the first connecting rod (113); the rotation axis connecting the first swing arm (112) and the first T-shaped rod (111) is perpendicular to and intersects the rotation axis connecting the moving platform (1) and the first T-shaped rod (111); The second three-axis parallel mechanism includes a moving platform (2); a first motion branch consisting of a first swing arm (211), a first T-shaped rod (212), a first connecting rod (213), and a first linear feed device, wherein the first linear feed device consists of a first slider (214) and a first guide rail (215); a second motion branch consisting of a second swing arm (221), a second T-shaped rod (222), a second connecting rod (223), and a second linear feed device, wherein the second linear feed device consists of a second slider (224) and a second guide rail (225); a third motion branch consisting of a third swing arm (231), a third T-shaped rod (232), a third connecting rod (233), and a third linear feed device, wherein the third linear feed device consists of a third slider (234) and a third guide rail (235); the first motion branch, the second motion branch, and the third motion branch have the same structure; One end of the moving platform (2) is connected to one end of the first swing arm (211) via a hinge with one degree of rotational freedom; the other end of the first swing arm (211) is connected to one end of the first T-shaped rod (212) via a hinge with one degree of rotational freedom; the other end of the first T-shaped rod (212) is connected to one end of the first connecting rod (213) via a hinge with one degree of rotational freedom; the other end of the first connecting rod (213) is connected to the first slider (214) via a hinge with one degree of rotational freedom; the first slider (214) is connected to the first guide rail (215) via a single-degree-of-freedom moving joint; the first guide rail (215) is fixedly connected to the static platform; The rotation axis connecting the first slider (214) and the first connecting rod (213) is perpendicular to and intersects the axis of the sliding joint connecting the first slider (214) and the first guide rail (215); and is perpendicular to and intersects the direction vector along the first connecting rod (213); the rotation axis connecting the first T-shaped rod (212) and the first swing arm (211) is perpendicular to and intersects the direction vector along the first connecting rod (213); and is perpendicular to and intersects the direction vector along the first swing arm (211); and is perpendicular to but does not intersect the rotation axis connecting the moving platform (2) and the first swing arm (211); the rotation axis connecting the moving platform (2) and the first swing arm (211) is perpendicular to and intersects the direction vector along the first swing arm (211).

2. The three-axis parallel mechanism according to claim 1, characterized in that, It includes at least one memory and at least one processor.

3. The three-axis parallel mechanism according to claim 1, characterized in that, The linear feed device includes the following linear drive types: motor lead screw, pneumatic or hydraulic device.

4. A method for forward and inverse kinematics of a triaxial parallel mechanism as described in claim 1, the method comprising the following steps: S1: Establish the forward and inverse kinematics model based on the first three-axis parallel mechanism, at the origin of the static platform. Establish a base coordinate system at the reference point at the end of the moving platform (1). A local connected coordinate system is established; the initial positions of the first guide rail (115), the second guide rail (125), and the third guide rail (135) are: The intersection points of the sliding joint axis connecting the first slider (114) and the first guide rail (115) with the rotation axis connecting the first connecting rod (113) and the first slider (114), the intersection points of the sliding joint axis connecting the second slider (124) and the second guide rail (125) with the rotation axis connecting the second connecting rod (123) and the second slider (124), and the intersection points of the sliding joint axis connecting the third slider (134) and the third guide rail (135) with the rotation axis connecting the third connecting rod (133) and the third slider (134) are: The points where the rotation axis connecting the first link (113) and the first swing arm (112) intersects with the direction vector along the first swing arm (112), the points where the rotation axis connecting the second link (123) and the second swing arm (122) intersects with the direction vector along the second swing arm (122), and the points where the rotation axis connecting the third link (133) and the third swing arm (132) intersects with the direction vector along the third swing arm (132) are: The points where the rotation axis connecting the moving platform (1) and the first T-shaped rod (111) intersects with the direction vector along the first swing arm (112), the points where the rotation axis connecting the moving platform (1) and the second T-shaped rod (121) intersects with the direction vector along the second swing arm (122), and the points where the rotation axis connecting the moving platform (1) and the third T-shaped rod (131) intersects with the direction vector along the third swing arm (132) are: ; S2: Obtain the attitude matrix of the moving platform (1) relative to the base coordinate system. End reference point Position vector in the base coordinate system The virtual circumcircle radius of the static platform 、Moving platform (1) Virtual circumscribed circle radius and branch offset angle ; S3: By using the aforementioned branch offset angle and coordinate transformation, the coordinates in the local reference frame are obtained. coordinates By and the attitude matrix Multiply and then sum Add them together to obtain the coordinates in the base coordinate system. coordinate; S4: According to the above coordinates and Coordinates can be used to obtain vectors. , The length of the first connecting rod (113) after taking the mold is always the same. Therefore, the first set of constraint equations can be obtained: ； S5: According to the above coordinates and Coordinates can be used to obtain vectors. , The length of the first swing arm (112) after taking the mold is always the same. Therefore, the second set of constraint equations can be obtained: ； S6: According to the above Coordinates can be used to obtain vectors ,in , and According to the above with vector Since they are perpendicular to each other, their dot product is zero. Therefore, we can derive the third set of constraint equations: ； S7: According to the above Coordinates can be used to obtain vectors ,in , and According to the above with vector Since they are perpendicular to each other, their dot product is zero. Therefore, we can derive the fourth set of constraint equations: ； S8: Based on the rotation axis connecting the first link (113) and the first swing arm (112), the rotation axis of the second link (123) and the second swing arm (122), the rotation axis of the third link (133) and the third swing arm (132), and the vector... Since they are perpendicular to each other, their dot product is zero. Therefore, we can derive the fifth set of constraint equations: ； S9: Establish the forward and inverse kinematics model based on the second three-axis parallel mechanism, and redefine the intersection points of the rotation axes connecting the first swing arm (211) and the first T-shaped rod (212) with the direction vector along the first connecting rod (213), the intersection points of the rotation axes of the second swing arm (221) and the second T-shaped rod (222) with the direction vector along the second connecting rod (223), and the intersection points of the rotation axes of the third swing arm (231) and the third T-shaped rod (232) with the direction vector along the third connecting rod (233). The intersection points of the rotation axis connecting the moving platform (2) and the first swing arm (211) with the direction vector along the first swing arm (211), the intersection points of the rotation axis connecting the moving platform (2) and the second swing arm (221) with the direction vector along the second swing arm (221), and the intersection points of the rotation axis connecting the moving platform (2) and the third swing arm (231) with the direction vector along the third swing arm (231) are redefined as follows: The process of establishing the first, second, third, and fourth constraint equation sets of the second three-axis parallel mechanism is consistent with steps S1, S2, S3, S4, S5, S6, and S7. S10: Based on the rotation axes of the first swing arm (211) and the first T-shaped rod (212), the rotation axes of the second swing arm (221) and the second T-shaped rod (222), the rotation axes of the third swing arm (231) and the third T-shaped rod (232), and the vector... Since they are perpendicular to each other, their dot product is zero. Therefore, we can derive the sixth set of constraint equations: ； S11: Based on the meaning of inverse kinematics, given the terminal trajectory of the moving platform (1), by simultaneously solving the first, second, third, fourth, and fifth constraint equations, the position coordinates of the first parallel mechanism can be solved. Given the end trajectory of the moving platform (2), by simultaneously solving the first, second, third, fourth, and sixth constraint equations, the position coordinates of the second parallel mechanism can be obtained. Based on the meaning of the correct kinematic solution, given the above... By combining the first, second, third, fourth, and fifth constraint equations, the terminal trajectory of the moving platform (1) can be solved; by combining the first, second, third, fourth, and sixth constraint equations, the terminal trajectory of the moving platform (2) can be solved.

5. The method for forward and inverse kinematics of a triaxial parallel mechanism according to claim 4, characterized in that, The process also includes the following steps: receiving an action command from the three-axis parallel mechanism, the action command including at least one of the following: translation, rotation; outputting a trajectory sequence based on the action command; outputting another action command based on the trajectory sequence; and setting the... The position vector is output to the motor servo system, enabling the motor servo system to control the three-axis parallel mechanism to complete the target motion trajectory; the end trajectory is output to the host computer system, enabling the host computer to obtain the end reference point pose of the three-axis parallel mechanism to complete motion control.

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