Quaternion joint design method and quaternion joint

Abstract

To improve accuracy of a link tip position.SOLUTION: In a design method of a quaternion joint including a first member, and a second member rotatably connected to the first member via a plurality of links, a distance hc between both ends of a link at an initial position of an operation angle of the link, a distance wc between the end portions of links adjacent to each other, and a distance h0 necessary for securing a degree of freedom in the end portions of the links, are determined on the basis of a constraint condition to make a distance between a point on an ellipse corresponding to a start end operation angle of the link and a point determined by deviating a center point of the ellipse by the distance h0, and a distance between a point on the ellipse corresponding to a terminal end operation angle of the link and a point determined by deviating the center point of the ellipse by the distance h0 agree with each other on an elliptical track drawn by intersection points of the links according to rotation of the second member.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present disclosure relates to a design method for a quaternion joint and a quaternion joint. [Background technology]

[0002] A method for designing a quaternion joint is known in which the link's operating angle of 0 deg is set as the median value, and parameters are analytically set so that when the operating angle is changed from there, the range of change in the distance (link length) between the point on the elliptical orbit drawn by the intersection of the links and the point shifted by a distance h0 from the center point of the ellipse is reduced (see, for example, Patent Document 1). [Prior art documents] [Patent documents]

[0003] [Patent Document 1] U.S. Patent Application Publication No. 2021 / 0197407 Summary of the Invention [Problem to be solved by the invention]

[0004] The distance between the point on the elliptical orbit described by the intersection of the above-mentioned links and the point shifted by a distance h0 from the center point of the ellipse changes depending on the operating angle of the link, but if the change in this distance is large, there is a risk that the accuracy of the link tip position will deteriorate.

[0005] The present disclosure has been made to solve such problems, and a main object of the present disclosure is to provide a quaternion joint and a design method for the quaternion joint that can improve the accuracy of the link tip positions. [Means for solving the problem]

[0006] In order to achieve the above object, one aspect of the present disclosure is to A first member; a second member rotatably connected to the first member via a plurality of links, The distance h between both ends of the link at the start operating angle of the link c , the distance between adjacent link ends w c and a distance h0 necessary to ensure the degree of freedom of the link end is set based on a constraint condition that, in an elliptical orbit described by the intersection of the link in response to the rotation of the second member, a distance between a point on the ellipse corresponding to a starting operating angle of the link and a point obtained by shifting the center point of the ellipse by the distance h0 coincides with a distance between a point on the ellipse corresponding to a terminal operating angle of the link and a point obtained by shifting the center point of the ellipse by the distance h0. How to design a quaternion joint is. In this embodiment, when the start end operating angle of the link is set to 0 deg and the end end operating angle of the link is set to 45 deg, the h is set to satisfy the following formula indicating the constraint condition. c , w c , and h0 may be set.

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[0007] According to the present disclosure, it is possible to provide a quaternion joint and a design method for a quaternion joint that can improve the accuracy of the link tip positions. [Brief explanation of the drawings]

[0008] [Figure 1] FIG. 2 is a schematic diagram of a quaternion joint according to the present embodiment. [Figure 2] FIG. 10 is a diagram illustrating the link length r(ψ) of a quaternion joint. [Figure 3] FIG. 2 is a side view of each link of the quaternion joint according to the present embodiment, illustrating each parameter. [Figure 4] 10 is a schematic diagram showing the state of each link when the start-end operating angle ψ1 of the link is set to 0 deg. FIG. [Figure 5] FIG. 10 is a schematic diagram showing the state of each link when the terminal operating angle ψ2 of the link is set to 45 degrees. [Figure 6] FIG. 10 is a diagram illustrating the relationship between parameters r and h and the size of a quaternion joint. [Figure 7] FIG. 10 is a diagram comparing the range of change in link length of a quaternion joint designed by the design method according to the present embodiment with the range of change in link length of a quaternion joint designed by a conventional design method. DETAILED DESCRIPTION OF THE INVENTION

[0009] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A quaternion joint according to an embodiment of the present invention is mounted on a joint such as a wrist joint of a robot.

[0010] 1 is a schematic diagram of a quaternion joint according to this embodiment. The quaternion joint 1 includes a first member 2 and a second member 4 rotatably connected to the first member 2 via a plurality of links 3 that intersect in a side view.

[0011] Both ends of each link 3 are connected to the end faces 21, 41 of the first and second members 2, 4, respectively, via a swing mechanism. The swing mechanism can swing the link 3 in any direction by rotating the link 3 around two first and second rotation axes that are arranged perpendicular to each other and stacked, as described below.

[0012] In the quaternion joint 1, virtual hemispherical shapes that are the trajectories of the intersection points X of the links 3 are formed on the end faces 21, 41 of the first and second members 2, 4, respectively, and the links 3 are arranged so that the second member 4 rotates while the hemispherical shapes come into contact with each other at the intersection points X. Note that in this embodiment, the number of links 3 is three, but is not limited to this, and any number may be used, such as two or four or more, as long as the above operating conditions are satisfied.

[0013] As shown in FIG. 2, the intersection point X of the link 3 describes an elliptical orbit in response to the rotation of the second member 4. The link length r(ψ) of the quaternion joint 1 is a point P0 (0, -h c ) and point P on the ellipse corresponding to the operating angle ψ of link 3 C (x c , y c ) The link length r(ψ) is calculated, for example, by the following equation (1).

[0014]

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[0015] However, the distance h between both ends of link 3 at the start operating angle of link 3 c , the distance between the ends of adjacent links 3 w c , length l of link 3 cand a distance h0 necessary to ensure the degree of freedom of the end of link 3. The start-end operating angle of link 3 is the operating angle ψ at the initial position of link 3. The distance h0 is, for example, the distance between the first and second rotation axes of the end of link 3, as will be described later.

[0016] Here, the link length r(ψ) changes depending on the operating angle ψ of the link 3. Conventionally, ψ=0 deg is set as the median value, and the above-mentioned parameter h is set to reduce the range of change from there. c , w c , h0 were analytically determined and set. Therefore, when the link length r(ψ) changed significantly, the accuracy of the link tip position deteriorated. Furthermore, for example, when a joint is driven by a wire, the wire length changes significantly depending on the operating angle ψ, and the stiffness of the joint also changes significantly. This can make control difficult because the positioning accuracy changes depending on the posture.

[0017] In contrast, in the design method of the quaternion joint 1 according to this embodiment, the above-mentioned parameter h c , w c , h0 are set based on the constraint that the link length r(ψ1) corresponding to the start operating angle ψ1 of the link 3 and the link length r(ψ2) corresponding to the end operating angle ψ2 of the link 3 are equal.

[0018] This reduces the variation range of the link length r(ψ) compared to conventional technology, improving the accuracy of the link tip position. Furthermore, it is possible to easily design optimal parameter values without using analytical methods such as parameter studies.

[0019] Furthermore, even when a joint is driven by a wire, the change in wire length due to the operating angle ψ can be kept small, and the change in joint stiffness can also be kept small. This improves positioning accuracy due to posture, thereby improving controllability.

[0020] Here, for example, if the starting operating angle ψ1 of link 3 is 0 deg (ψ1 = 0 deg) and the terminal operating angle ψ2 of link 3 is 45 deg (ψ2 = 45 deg), the constraint condition for matching the link length r(ψ1) corresponding to the starting operating angle ψ1 of link 3 and the link length r(ψ2) corresponding to the terminal operating angle ψ2 of link 3 is given by the following equation (2). The terminal operating angle ψ2 of link 3 is the operating angle ψ2 at the terminal position of link 3.

[0021] As described above, the terminal motion angle of the link 3 is set to ψ2=45 deg, taking into consideration the maximum motion angle of the quaternion joint 1.

[0022] Therefore, the parameter h is set to satisfy the constraint (2). c , w c , and h0, the range of change in the link length r(ψ) can be reduced compared to the prior art, taking into account the maximum operating angle of the quaternion joint 1, thereby improving the accuracy of the link tip position.

[0023]

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[0024] Next, a method for deriving the above formula (2) will be described in detail. Fig. 3 is a side view of each link of the quaternion joint according to this embodiment, and is a diagram for explaining each parameter. Each parameter is set as shown in Fig. 3.

[0025] The parameters shown in FIG. 1 and the parameters shown in FIG. 3 are respectively h c =l, w c / 2=r, h0=h. The distance h is the distance between the first and second rotation axes 31 and 32 at the ends of the link 3, which are arranged perpendicular to each other and stacked on top of each other.

[0026] Fig. 4 is a schematic diagram showing the state of each link when the link start operating angle ψ1 is 0 deg (ψ1 = 0 deg), and Fig. 5 is a schematic diagram showing the state of each link when the link end operating angle ψ2 is 45 deg (ψ2 = 45 deg).

[0027] As a characteristic of the mechanism, the center distance (l+2r) does not change. The inclination of the end face 21 of the first member 2 and the end face 41 of the second member 4 relative to the central axis is always the same.

[0028] Focusing on the triangle (hatched portion) shown in FIG. 5, the following equations (3) and (4) are derived from the geometric relationship.

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[0029] The following equations (5) and (6) are derived from the above equation (3).

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[0030] By substituting the above formula (6) into the above formula (4), the following formula (7) is derived.

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[0031] By substituting the above equation (5) into the above equation (7), the following equation (8) is derived. c =l, w c Since / 2=r and h0=h, the following equation (8) is the same as the above equation (2).

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[0032] In the above description, the start operating angle ψ1 of the link 3 is set to 0 degrees (ψ1=0 degrees) and the end operating angle ψ2 of the link 3 is set to 45 degrees (ψ2=45 degrees), but this is not limiting.

[0033] For example, the terminal operating angle ψ2 of the link 3 may be set to an angle between 40 and 45 degrees. In this case, too, the equation of the constraint condition can be calculated from the geometric relationship, as in the case where the terminal operating angle ψ2 of the link 3 is 45 degrees.

[0034] Here, by setting the parameters l, r, and h so as to satisfy the above formula (8), the range of change in link length r (ψ) can be reduced. However, the lower limit of r is determined by interference with link 3, and as shown in Figure 5, the lower limit of l is determined by interference with the upper and lower pulleys when bent by 90 degrees (ψ2 = 45 degrees). For this reason, an appropriate h must be selected within the range of the lower limits of r and l.

[0035] Figure 6 is a diagram showing the relationship between the parameters r and h and the size of the quaternion joint. Figure 6 shows the results of measuring the size of the quaternion joint while changing the parameter h in the range of 2.5 mm to 3.5 mm. Note that since the parameters h and r are small values, fractional adjustment is performed by 1 for processing accuracy reasons.

[0036] As shown in Fig. 6, as the value of parameter h increases, the size of quaternion joint 1 decreases. Also, as the value of parameter r increases, the size of quaternion joint 1 increases. By explicitly determining the relationship shown in Fig. 6, it is possible to select an appropriate h within the lower limit range of r and l above.

[0037] Next, a description will be given of the variation range of the link length r(ψ) of a quaternion joint designed by the quaternion joint design method according to this embodiment.

[0038] As described above, FIG. 7 is a diagram comparing the range of change in link length of a quaternion joint designed by the design method according to this embodiment with the range of change in link length of a quaternion joint designed by a conventional design method.

[0039] 7, it can be seen that the range of variation in link length r(ψ) of quaternion joint 1 designed by the design method according to this embodiment has a smaller difference between the maximum and minimum values than the range of variation in link length r(ψ) of a quaternion joint designed by a conventional design method. In other words, by designing quaternion joint 1 by the design method according to this embodiment, the range of variation in link length r(ψ) of quaternion joint 1 can be reduced, and the accuracy of the link tip positions can be improved.

[0040] As described above, in the design method of the quaternion joint 1 according to this embodiment, the distance h between the end face 21 of the first member 2 and the end face 41 of the second member 4 at the start end operating angle ψ1 of the link 3 is c , the distance between the ends of adjacent links w c , and the distance h0 required to ensure the degree of freedom of the link end is set based on a constraint condition that matches the distance on the ellipse corresponding to the starting operating angle ψ1 of the link 3 and the point obtained by shifting the center point O of the ellipse by the distance h0 in the elliptical orbit described by the intersection point X of the link 3 in response to the rotation of the second member 4, and the distance on the ellipse corresponding to the terminal operating angle ψ2 of the link and the point obtained by shifting the center point O of the ellipse by the distance h0.

[0041] This makes it possible to reduce the variation range of the link length r(ψ), thereby improving the accuracy of the link tip position.

[0042] Although several embodiments of the present disclosure have been described, these embodiments are presented as examples and are not intended to limit the scope of the invention. These novel embodiments can be embodied in various other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their modifications are included within the scope and spirit of the invention, and are also included in the scope of the invention and its equivalents as defined in the claims. [Explanation of symbols]

[0043] 1 quaternion joint, 2 first member, 3 links, 4 second member, 21 End face, 41 End face

Claims

1. A first member; a second member rotatably connected to the first member via a plurality of links, The distance h between both ends of the link at the start end operating angle of the link ｃ , the distance between adjacent link ends w ｃ , and the distance h necessary to ensure the degree of freedom of the link end ０ The distance h is the distance between the point on the ellipse corresponding to the start end operation angle of the link and the center point of the ellipse in the elliptical orbit drawn by the intersection of the link in response to the rotation of the second member. ０ The distance between the point on the ellipse corresponding to the terminal operating angle of the link and the center point of the ellipse is the distance h ０ The distance between the point and the point shifted by the distance is set based on the constraint that matches the distance. When the start operating angle of the link is 0 deg and the end operating angle of the link is 45 deg, h c , w c , and h 0 are set so as to satisfy the following formula indicating the constraint condition: [Equation 8] How to design quaternion joints.

2. A first member; a second member rotatably connected to the first member via a plurality of links, The distance h between both ends of the link at the start end operating angle of the link ｃ , the distance between adjacent link ends w ｃ , and the distance h necessary to ensure the degree of freedom of the link end ０ In the elliptical orbit drawn by the intersection of the link in response to the rotation of the second member, the point on the ellipse corresponding to the start end operation angle of the link and the center point of the ellipse are separated by the distance h ０ The distance between the point on the ellipse corresponding to the terminal operating angle of the link and the center point of the ellipse is the distance h ０ The distance between the point and the point shifted by 1 is set based on the constraint that matches the distance, When the start operating angle of the link is 0 deg and the end operating angle of the link is 45 deg, h c , w c , and h 0 are set so as to satisfy the following formula indicating the constraint condition: [Equation 8] Quaternion joint.

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