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

Abstract

The invention relates to a position forward and inverse solution method of a three-axis parallel mechanism and the three-axis parallel mechanism. The invention discloses three-axis parallel mechanisms. A first three-axis parallel mechanism comprises a movable platform; a first T-shaped rod, a first swing arm, a first connecting rod and a first linear feeding device form a first motion branch chain, and the first linear feeding device is composed of a first sliding block and a first guide rail. A second T-shaped rod, a second swing arm, a second connecting rod and a second linear feeding device form a second motion branch chain, and the second linear feeding device is composed of a second sliding block and a second guide rail. A third T-shaped rod, a third swing arm, a third connecting rod and a third linear feeding device form a third motion branch chain, and the third linear feeding device is composed of a third sliding block and a third guide rail. The first movement branch chain, the second movement branch chain and the third movement branch chain are the same in structure. The method is a numerical solution method combined with the robotics theory and has high solution precision.

Description

Technical Field

[0001] The present invention relates to the technical field of robots, and particularly to a method for solving forward and inverse position solutions of a three-axis parallel mechanism and a three-axis parallel mechanism. Background Art

[0002] At present, a three-axis parallel mechanism with two rotational degrees of freedom and one translational degree of freedom is a very important type of parallel mechanism with few degrees of freedom. Such a parallel mechanism has advantages such as a large stiffness-to-mass ratio, high load capacity, and compact structure, and can effectively save the costs of system design, manufacturing, and control in engineering practice.

[0003] The most common currently spatial one-translation two-rotation parallel mechanism includes a static platform, a moving platform, and three identical branched chains. The branched chains of this parallel mechanism are evenly distributed circumferentially in space, the end effector is fixedly connected to the moving platform, and the guide rail direction is parallel to the z-axis feeding direction. In the parallel mechanism adopting this structural form, each branched chain can independently move linearly under the drive of a feeding device, such as a combined structure of a servo motor and a ball screw pair, so that the moving platform generates a translation along the axis of symmetry and two rotations around two orthogonal axes perpendicular to this axis relative to the fixed frame.

[0004] In order to develop a control system for a new type of parallel mechanism and achieve precise motion control of the parallel mechanism, and thus finally complete high-precision machining, the forward and inverse solution algorithms of the parallel mechanism are the first problems to be solved. The forward and inverse solution algorithms can be used for work such as workspace analysis, end trajectory analysis, structural design of components, and selection of standard parts of a robot before production and manufacturing, and are also an important link for enabling the parallel mechanism to perform high-precision machining along a specified end trajectory.

[0005] However, existing commercial simulation software is closed-source software, which enables designers to only obtain its calculation results and cannot deeply understand the operating principle of the parallel mechanism, bringing limitations to mechanism design and motion control. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method for solving forward and inverse position solutions 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 includes a moving platform. The first T-shaped rod, the first swing arm, the first connecting rod, and the first linear feed device form a first kinematic chain. The first linear feed device is composed of a first slider and a first guide rail. The second T-shaped rod, the second swing arm, the second connecting rod, and the second linear feed device form a second kinematic chain. The second linear feed device is composed of a second slider and a second guide rail. The third T-shaped rod, the third swing arm, the third connecting rod, and the third linear feed device form a third kinematic chain. The third linear feed device is composed of a third slider and a third guide rail. The first kinematic chain, the second kinematic chain, and the third kinematic chain have the same structure.

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

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

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

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

[0012] The axis of rotation connecting the first slider (the second slider / the third slider) and the first connecting rod (the second connecting rod / the third connecting rod) is perpendicular and intersects with the axis of the moving pair connecting the first slider (the second slider / the third slider) and the first guide rail (the second guide rail / the third guide rail); and is perpendicular and intersects with the direction vector along the first connecting rod (the second connecting rod / the third connecting rod); the axis of rotation connecting the first T-shaped rod (the second T-shaped rod / the third T-shaped rod) and the first swing arm (the second swing arm / the third swing arm) is perpendicular and intersects with the direction vector along the first connecting rod (the second connecting rod / the third connecting rod); and is perpendicular and intersects with the direction vector along the first swing arm (the second swing arm / the third swing arm); and is perpendicular and non-intersecting with the axis of rotation connecting the moving platform and the first swing arm (the second swing arm / the third swing arm); the axis of rotation connecting the moving platform and the first swing arm (the second swing arm / the third swing arm) is perpendicular and intersects with the direction vector along the first swing arm (the second swing arm / the third swing arm).

[0013] A method for forward and inverse position solutions of a three-axis parallel mechanism includes the following steps:

[0014] S1: Establish the forward and inverse kinematic models based on the first three-axis parallel mechanism. Establish a base coordinate system at the origin O of the static platform and a local body coordinate system at the end reference point Q of the moving platform. The initial positions of the first guide rail, the second guide rail, and the third guide rail are B i , i = 1, 2, 3; The intersection of the moving pair axis connecting the first slider and the first guide rail and the rotation axis connecting the first link and the first slider, the intersection of the moving pair axis connecting the second slider and the second guide rail and the rotation axis connecting the second link and the second slider, and the intersection of the moving pair axis connecting the third slider and the third guide rail and the rotation axis connecting the third link and the third slider are P i , i = 1, 2, 3; The intersection of the rotation axis connecting the first link and the first swing arm and the direction vector along the first swing arm, the intersection of the rotation axis connecting the second link and the second swing arm and the direction vector along the second swing arm, and the intersection of the rotation axis connecting the third link and the third swing arm and the direction vector along the third swing arm are C i , i = 1, 2, 3; The intersection of the rotation axis connecting the moving platform and the first T-shaped rod and the direction vector along the first swing arm, the intersection of the rotation axis connecting the moving platform and the second T-shaped rod and the direction vector along the second swing arm, and the intersection of the rotation axis connecting the moving platform and the third T-shaped rod and the direction vector along the third swing arm are A i , i = 1, 2, 3.

[0015] S2: Obtain the attitude matrix R of the moving platform relative to the base coordinate system, the position vector r of the end reference point Q in the base coordinate system Q , the virtual circumradius b of the static platform, the virtual circumradius a of the moving platform, and the offset angle β of the branch chain i , i = 1, 2, 3.

[0016] S3: Through the position offset angle and coordinate transformation, obtain the coordinates of A i in the local reference system as A i0 , i = 1, 2, 3. After multiplying by the attitude matrix R and then adding r Q , obtain the coordinates of A i in the base coordinate system.

[0017] S4: According to the coordinates of P i and the coordinates of C i , the vector can be obtained . After taking the modulus, it is always the length l of the first link (113) 1 . Thus, the first constraint equation set can be obtained:

[0018]

[0019] S5: According to the Ai Coordinate sum C i Given the coordinates, a vector can be obtained After taking the modulus, it is always the length l of the first swing arm (112) 2 , from which a second constraint equation set can be obtained:

[0020]

[0021] S6: According to the said A i coordinates, a vector can be obtained where m = 1, 2, 3, n = 1, 2, 3 and i ≠ m ≠ n; According to the said and the vector are perpendicular to each other and the dot product is zero, from which a third constraint equation set can be obtained:

[0022]

[0023] S7: According to the said B i coordinates, a vector can be obtained where m = 1, 2, 3, n = 1, 2, 3 and i ≠ m ≠ n; According to the said and the vector are perpendicular to each other and the dot product is zero, from which a fourth constraint equation set can be obtained:

[0024]

[0025] S8: According to the rotational axes connecting the first link and the first swing arm, the second link and the second swing arm, the third link and the third swing arm and the vector are perpendicular to each other and the dot product is zero, from which a fifth constraint equation set can be obtained:

[0026]

[0027] S9: Establish a forward and inverse kinematics model for the second three-axis parallel mechanism, and redefine the intersection points of the rotational axes connecting the first swing arm and the first T-shaped rod and the direction vector along the first link, the rotational axes connecting the second swing arm and the second T-shaped rod and the direction vector along the second link, the rotational axes connecting the third swing arm and the third T-shaped rod and the direction vector along the third link as C i ; Redefine the intersection points of the rotational axes connecting the moving platform and the first swing arm and the direction vector along the first swing arm, the rotational axes connecting the moving platform and the second swing arm and the direction vector along the second swing arm, the rotational axes connecting the moving platform and the third swing arm and the direction vector along the third swing arm as A i ; The remaining content is consistent with steps S1, S2, S3, S4, S5, S6 and S7

[0028] S10: according to the rotation axis of the first swing arm and the first T-shaped rod, the rotation axis of the second swing arm and the second T-shaped rod, the rotation axis of the third swing arm and the third T-shaped rod and the vector They are perpendicular to each other, and the dot product is zero, so we can get the sixth constraint equation group:

[0029]

[0030] S11: According to the meaning of the inverse solution of kinematics, given the end trajectory of the moving platform, the first constraint equation group, the second constraint equation group, the third constraint equation group, the fourth constraint equation group and the fifth constraint equation group are combined to solve the position coordinate P of the first parallel mechanism. i Given the end trajectory of the moving platform, the first constraint equation group, the second constraint equation group, the third constraint equation group, the fourth constraint equation group and the sixth constraint equation group can be solved to obtain the position coordinate P of the second parallel mechanism. i According to the meaning of the kinematic solution, given the P i Coordinates, the first constraint equation group, the second constraint equation group, the third constraint equation group, the fourth constraint equation group and the fifth constraint equation group are combined to solve the terminal trajectory of the moving platform; the first constraint equation group, the second constraint equation group, the third constraint equation group, the fourth constraint equation group and the sixth constraint equation group are combined to solve the terminal trajectory of the moving platform.

[0031] The method further comprises the following steps: receiving an action instruction of the three-axis parallel mechanism, the action instruction comprising at least one of the following: translation, rotation; outputting a trajectory sequence according to the action instruction; outputting an action instruction according to the trajectory sequence; converting the P i The position vector is output to the motor servo system, so that the motor servo system controls the three-axis parallel mechanism to complete the target motion trajectory; the terminal trajectory is output to the host computer system, so that the host computer obtains the terminal reference point posture of the three-axis parallel mechanism to complete the motion control. The iterative method includes but is not limited to the Newton-Raphson numerical method.

[0032] In a second aspect, 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 forward and inverse position solution method of the three-axis parallel mechanism of the first aspect of the present invention. The linear feed system in the three-axis parallel mechanism includes the following linear drive forms: motor screw, pneumatic or hydraulic device.

[0033] The advantages and positive effects of the present invention are:

[0034] 1. The branches of the three-axis parallel mechanism are evenly distributed circumferentially in space. Compared with serial robots, it has a large stiffness-to-mass ratio and strong load capacity. The three-axis parallel mechanism has a compact structure and small volume, and can be used as a power module for plug-and-play, which can further meet the requirements of integrated design and manufacturing.

[0035] 2. The forward and inverse kinematic algorithms can be used for tasks such as workspace analysis, end-effector trajectory analysis, structural design of components, and selection of standard parts before robot production and manufacturing. At the same time, it is also an important part for the parallel mechanism to perform high-precision machining along the specified end-effector trajectory through the control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a schematic structural diagram of the first three-axis parallel mechanism;

[0037] Figure 2 is a schematic structural diagram of the second three-axis parallel mechanism;

[0038] Figure 3 is a schematic diagram of the coordinate system and reference points of the first three-axis parallel mechanism;

[0039] Figure 4 is a schematic diagram of the coordinate system and reference points of the second three-axis parallel mechanism;

[0040] Figure 5 is a schematic structural diagram of the branches of the first three-axis parallel mechanism;

[0041] Figure 6 is a schematic structural diagram of the branches of the second three-axis parallel mechanism;

[0042] Figure 7 is a schematic diagram of Structure 1 of the invention embodiment;

[0043] Figure 8 is a schematic diagram of Structure 2 of the invention embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0044] The forward and inverse kinematic methods of the three-axis parallel mechanism and the three-axis parallel mechanism will be described in detail below with reference to the drawings and embodiments.

[0045] As Figure 1-8As shown, the first three-axis parallel mechanism includes a moving platform 1; the first T-shaped rod 111, the first swing arm 112, the first connecting rod 113, and the first linear feed device form the first kinematic chain. The first linear feed device is composed of a first slider 114 and a first guide rail 115; the second T-shaped rod 121, the second swing arm 122, the second connecting rod 123, and the second linear feed device form the second kinematic chain. The second linear feed device is composed of a second slider 124 and a second guide rail 125; the third T-shaped rod 131, the third swing arm 132, the third connecting rod 133, and the third linear feed device form the third kinematic chain. The first kinematic chain, the second kinematic chain, and the third kinematic chain have the same structure.

[0046] One end of the moving platform 1 is connected to one end of the first T-shaped rod 111 (the second T-shaped rod 121 / the third T-shaped rod 131) through a hinge with one degree of rotational freedom; the other end of the first T-shaped rod 111 (the second T-shaped rod 121 / the third T-shaped rod 131) is connected to one end of the first swing arm 112 (the second swing arm 122 / the third swing arm 132) through a hinge with one degree of rotational freedom; the other end of the first swing arm 112 (the second swing arm 122 / the third swing arm 132) is connected to one end of the first connecting rod 113 (the second connecting rod 123 / the third connecting rod 133) through a hinge with one degree of rotational freedom; the other end of the first connecting rod 113 (the second connecting rod 123 / the third connecting rod 133) is connected to the first slider 114 (the second slider 124 / the third slider 134) through a hinge with one degree of rotational freedom; the first slider 114 (the second slider 124 / the third slider 134) is connected to the first guide rail 115 (the second guide rail 125 / the third guide rail 135) through a single-degree-of-freedom moving joint; the first guide rail 115 (the second guide rail 125 / the third guide rail 135) is fixedly connected to the static platform.

[0047] 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 and intersects with the moving pair axis 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 and intersects with the direction vector along the first connecting rod 113 (second connecting rod 123 / third connecting rod 133); and is perpendicular but does not intersect with 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 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) is perpendicular and intersects with 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 and intersects with 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 and intersects with 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).

[0048] The second three-axis parallel mechanism includes a moving platform 2; the first swing arm 211, the first T-shaped rod 212, the first connecting rod 213, and the first linear feed device form the first motion branch chain, and the first linear feed device is composed of a first slider 214 and a first guide rail 215; the second swing arm 221, the second T-shaped rod 222, the second connecting rod 223, and the second linear feed device form the second motion branch chain, and the second linear feed device is composed of a second slider 224 and a second guide rail 225; the third swing arm 231, the third T-shaped rod 232, the third connecting rod 233, and the third linear feed device form the third motion branch chain, and the third linear feed device is composed of a third slider 234 and a third guide rail 235; the first motion branch chain, the second motion branch chain, and the third motion branch chain have the same structure.

[0049] One end of the moving platform 2 is connected to one end of the first swing arm 211 (the second swing arm 221 / the third swing arm 231) through a hinge with one degree of rotational freedom; the other end of the first swing arm 211 (the second swing arm 221 / the third swing arm 231) is connected to one end of the first T-shaped rod 212 (the second T-shaped rod 222 / the third T-shaped rod 232) through a hinge with one degree of rotational freedom; the other end of the first T-shaped rod 212 (the second T-shaped rod 222 / the third T-shaped rod 232) is connected to one end of the first connecting rod 213 (the second connecting rod 223 / the third connecting rod 233) through a hinge with one degree of rotational freedom; the other end of the first connecting rod 213 (the second connecting rod 223 / the third connecting rod 233) is connected to the first slider 214 (the second slider 224 / the third slider 234) through a hinge with one degree of rotational freedom; the first slider 214 (the second slider 224 / the third slider 234) is connected to the first guide rail 215 (the second guide rail 225 / the third guide rail 235) through a single-degree-of-freedom moving joint; the first guide rail 215 (the second guide rail 225 / the third guide rail 235) is fixedly connected to the static platform.

[0050] The rotational axis connecting the first slider 214 (the second slider 224 / the third slider 234) and the first connecting rod 213 (the second connecting rod 223 / the third connecting rod 233) is perpendicular and intersects with the moving pair axis connecting the first slider 214 (the second slider 224 / the third slider 234) and the first guide rail 215 (the second guide rail 225 / the third guide rail 235); and is perpendicular and intersects with the direction vector along the first connecting rod 213 (the second connecting rod 223 / the third connecting rod 233); the rotational axis connecting the first T-shaped rod 212 (the second T-shaped rod 222 / the third T-shaped rod 232) and the first swing arm 211 (the second swing arm 221 / the third swing arm 231) is perpendicular and intersects with the direction vector along the first connecting rod 213 (the second connecting rod 223 / the third connecting rod 233); and is perpendicular and intersects with the direction vector along the first swing arm 211 (the second swing arm 221 / the third swing arm 231); and is perpendicular and non-intersecting with the rotational axis connecting the moving platform 2 and the first swing arm 211 (the second swing arm 221 / the third swing arm 231); the rotational axis connecting the moving platform 2 and the first swing arm 211 (the second swing arm 221 / the third swing arm 231) is perpendicular and intersects with the direction vector along the first swing arm 211 (the second swing arm 221 / the third swing arm 231).

[0051] For the three-axis parallel mechanism described in the above embodiments, the present invention also provides a method for forward and inverse position solutions of the three-axis parallel mechanism. The method will be introduced in detail below:

[0052] S1: Establish the forward and inverse kinematic models of the first three-axis parallel mechanism. Establish a base coordinate system at the origin O of the static platform, and establish a local body coordinate system at the end reference point Q of the moving platform 1. The initial positions of the first guide rail 115, the second guide rail 125, and the third guide rail 135 are B i , i = 1, 2, 3; The intersection point of the moving pair axis connecting the first slider 114 and the first guide rail 115 and the rotation axis connecting the first link 113 and the first slider 114, the intersection point of the moving pair axis connecting the second slider 124 and the second guide rail 125 and the rotation axis connecting the second link 123 and the second slider 124, and the intersection point of the moving pair axis connecting the third slider 134 and the third guide rail 135 and the rotation axis connecting the third link 133 and the third slider 134 are P i , i = 1, 2, 3; The intersection point of the rotation axis connecting the first link 113 and the first swing arm 112 and the direction vector along the first swing arm 112, the intersection point of the rotation axis connecting the second link 123 and the second swing arm 122 and the direction vector along the second swing arm 122, and the intersection point of the rotation axis connecting the third link 133 and the third swing arm 132 and the direction vector along the third swing arm 132 are C i , i = 1, 2, 3; The intersection point of the rotation axis connecting the moving platform 1 and the first T-shaped rod 111 and the direction vector along the first swing arm 112, the intersection point of the rotation axis connecting the moving platform 1 and the second T-shaped rod 121 and the direction vector along the second swing arm 122, and the intersection point of the rotation axis connecting the moving platform 1 and the third T-shaped rod 131 and the direction vector along the third swing arm 132 are A i , i = 1, 2, 3.

[0053] S2: Obtain the attitude matrix R of the moving platform 1 relative to the base coordinate system, the position vector r of the end reference point Q in the base coordinate system Q , the virtual circumradius b of the static platform, the virtual circumradius a of the moving platform 1, and the offset angle β of the branch chain i , i = 1, 2, 3.

[0054] S3: Through the position offset angle and coordinate transformation, obtain the coordinates of A i in the local reference system A i0 , i = 1, 2, 3. After multiplying by the attitude matrix R and then adding r Q , obtain the coordinates of A i in the base coordinate system.

[0055] S4: According to the coordinates of P i and the coordinates of C i , the vector can be obtained After taking the modulus, it is always the length l of the first link (113)1 , from which the first constraint equation set can be obtained:

[0056]

[0057] S5: According to the A i coordinates and C i coordinates, the vector is always the length l of the first swing arm (112) after taking the modulus 2 , from which the second constraint equation set can be obtained:

[0058]

[0059] S6: According to the A i coordinates, the vector can be obtained, where m = 1, 2, 3, n = 1, 2, 3 and i ≠ m ≠ n; according to the and the vector are perpendicular to each other, and the dot product is zero. From this, the third constraint equation set can be obtained:

[0060]

[0061] S7: According to the B i coordinates, the vector can be obtained, where m = 1, 2, 3, n = 1, 2, 3 and i ≠ m ≠ n; according to the and the vector are perpendicular to each other, and the dot product is zero. From this, the fourth constraint equation set can be obtained:

[0062]

[0063] S8: According to the rotation axes connecting the first link 113 and the first swing arm 112, the second link 123 and the second swing arm 122, the third link 133 and the third swing arm 132, and the vector are perpendicular to each other, and the dot product is zero. From this, the fifth constraint equation set can be obtained:

[0064]

[0065] S9: Establish the forward and inverse kinematics models of 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, the second swing arm 221 and the second T-shaped rod 222, the third swing arm 231 and the third T-shaped rod 232, and the direction vectors along the first link 213, the second link 223, and the third link 233 as C iRedefine the intersection of the rotation axis connecting the moving platform 2 and the first swing arm 211 and the direction vector along the first swing arm 211, the intersection of the rotation axis connecting the moving platform 2 and the second swing arm 221 and the direction vector along the second swing arm 221, and the intersection of the rotation axis connecting the moving platform 2 and the third swing arm 231 and the direction vector along the third swing arm 231 as A i ; The rest of the content remains consistent with step S1, step S2, step S3, step S4, step S5, step S6 and step S7.

[0066] S10: According to the rotation axis of the first swing arm 211 and the first T-shaped rod 212, the rotation axis of the second swing arm 221 and the second T-shaped rod 222, the rotation axis of the third swing arm 231 and the third T-shaped rod 232 and the vector They are perpendicular to each other, and the dot product is zero, so we can get the sixth constraint equation group:

[0067]

[0068] S11: According to the meaning of the inverse solution of kinematics, given the end trajectory of the moving platform 1, the first constraint equation group, the second constraint equation group, the third constraint equation group, the fourth constraint equation group and the fifth constraint equation group are combined to solve the position coordinate P of the first parallel mechanism. i Given the end trajectory of the moving platform 2, the first constraint equation group, the second constraint equation group, the third constraint equation group, the fourth constraint equation group and the sixth constraint equation group are combined to solve the position coordinate P of the second parallel mechanism. i According to the meaning of the kinematic solution, given the P i Coordinates, the first constraint equation group, the second constraint equation group, the third constraint equation group, the fourth constraint equation group and the fifth constraint equation group can be solved for the terminal trajectory of moving platform 1; the first constraint equation group, the second constraint equation group, the third constraint equation group, the fourth constraint equation group and the sixth constraint equation group can be solved for the terminal trajectory of moving platform 2.

[0069] Embodiment: An operator controls the movement of the three-axis parallel mechanism through a control system, and the software part of the control system includes the position forward and inverse solution algorithm of the present invention. The following steps are included: receiving an action instruction of the three-axis parallel mechanism, the action instruction includes at least one of the following: translation, rotation; outputting a trajectory sequence according to the action instruction; outputting an action instruction according to the trajectory sequence; outputting the position vector of the linear feed device to the motor servo system, so that the motor servo system controls the three-axis parallel mechanism to complete the target motion trajectory. The terminal trajectory is output to the host computer system, so that the host computer obtains the terminal reference point posture of the three-axis parallel mechanism to complete the motion control. Thereby finally controlling the three-axis parallel mechanism to complete the machining. As shown in FIG. Figure 7 and Figure 8As shown, the three-axis parallel mechanism can form a parallel power head with the static platform. As a plug-and-play processing module, it can further meet the requirements of integrated processing.

[0070] Although the embodiments of the present invention have been described above, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many forms without departing from the spirit of the present invention and the scope protected by the claims. These all fall within the protection scope of the present invention.

Claims

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

2. The three-axis parallel mechanism according to claim 1, characterized in that: 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 system includes the following linear drive forms: motor screw, pneumatic or hydraulic device.

4. A forward and inverse position solution method for a three-axis parallel mechanism as claimed in claim 1, the method comprising the following steps: S1: Establish a forward and inverse kinematics model based on the first three-axis parallel mechanism, establish a base coordinate system at the origin O of the static platform, and establish a local connected coordinate system at the end reference point Q of the moving platform (1); the initial positions of the first guide rail (115), the second guide rail (125) and the third guide rail (135) are B i , i=1,2,3; the intersection of the secondary axis of movement connecting the first slider (114) and the first guide rail (115) and the rotation axis connecting the first connecting rod (113) and the first slider (114), the intersection of the secondary axis of movement connecting the second slider (124) and the second guide rail (125) and the rotation axis connecting the second connecting rod (123) and the second slider (124), and the intersection of the secondary axis of movement connecting the third slider (134) and the third guide rail (135) and the rotation axis connecting the third connecting rod (133) and the third slider (134) is P i , i=1,2,3; the intersection of the rotation axis connecting the first connecting rod (113) and the first swing arm (112) and the direction vector along the first swing arm (112), the intersection of the rotation axis connecting the second connecting rod (123) and the second swing arm (122) and the direction vector along the second swing arm (122), and the intersection of the rotation axis connecting the third connecting rod (133) and the third swing arm (132) and the direction vector along the third swing arm (132) is C i , i=1, 2, 3; the intersection of the rotation axis connecting the moving platform (1) and the first T-shaped rod (111) and the direction vector along the first swing arm (112), the intersection of the rotation axis connecting the moving platform (1) and the second T-shaped rod (121) and the direction vector along the second swing arm (122), and the intersection of the rotation axis connecting the moving platform (1) and the third T-shaped rod (131) and the direction vector along the third swing arm (132) is A i ,i=1,2,3; S2: Obtain the posture matrix R of the moving platform (1) relative to the base coordinate system and the position vector r of the end reference point Q in the base coordinate system Q , the virtual circumscribed circle radius b of the static platform, the virtual circumscribed circle radius a of the dynamic platform (1) and the branch chain offset angle β i ,i=1,2,3; S3: Through the position offset angle and coordinate transformation, we can obtain A in the local reference system. i Coordinates of A i0 , i = 1, 2, 3, multiplied by the posture matrix R and then r Q Add them together to get A in the base coordinate system i coordinate; S4: According to the P i Coordinates and C i Coordinates, we get vector After modulo, it is always the length l1 of the first connecting rod (113), from which the first constraint equation group can be obtained: S5: According to the A i Coordinates and C i Coordinates, we get vector After modulo, it is always the length l2 of the first swing arm (112), from which the second constraint equation group can be obtained: S6: According to the A i Coordinates can be obtained vector Where m=1,2,3, n=1,2,3 and i≠m≠n; according to the With vector They are perpendicular to each other, and the dot product is zero, so we can get the third set of constraint equations: S7: According to the B i Coordinates can be obtained vector Where m=1,2,3, n=1,2,3 and i≠m≠n; according to the With vector They are perpendicular to each other, and the dot product is zero, so we can get the fourth set of constraint equations: S8: According to the rotation axis connecting the first connecting rod (113) and the first swing arm (112), the rotation axis of the second connecting rod (123) and the second swing arm (122), the rotation axis of the third connecting rod (133) and the third swing arm (132) and the vector They are perpendicular to each other, and the dot product is zero, so we can get the fifth set of constraint equations: S9: Establish a forward and inverse kinematics model based on the second three-axis parallel mechanism, and redefine the intersection of the rotation axis connecting the first swing arm (211) and the first T-shaped rod (212) and the direction vector along the first connecting rod (213), the intersection of the rotation axis of the second swing arm (221) and the second T-shaped rod (222) and the direction vector along the second connecting rod (223), and the intersection of the rotation axis of the third swing arm (231) and the third T-shaped rod (232) and the direction vector along the third connecting rod (233) as C. i ; The intersection of the rotation axis connecting the moving platform (2) and the first swing arm (211) and the direction vector along the first swing arm (211), the intersection of the rotation axis connecting the moving platform (2) and the second swing arm (221) and the direction vector along the second swing arm (221), and the intersection of the rotation axis connecting the moving platform (2) and the third swing arm (231) and the direction vector along the third swing arm (231) are redefined as A i ; The rest of the content is consistent with the steps S1, S2, S3, S4, S5, S6 and S7; S10: According to the rotation axis of the first swing arm (211) and the first T-shaped rod (212), the rotation axis of the second swing arm (221) and the second T-shaped rod (222), the rotation axis of the third swing arm (231) and the third T-shaped rod (232) and the vector They are perpendicular to each other, and the dot product is zero, so we can get the sixth constraint equation group: S11: According to the meaning of the inverse solution of kinematics, given the end trajectory of the moving platform (1), the first constraint equation group, the second constraint equation group, the third constraint equation group, the fourth constraint equation group and the fifth constraint equation group are combined to solve the position coordinate P of the first parallel mechanism. i Given the end trajectory of the moving platform (2), the first constraint equation group, the second constraint equation group, the third constraint equation group, the fourth constraint equation group and the sixth constraint equation group are combined to solve the position coordinate P of the second parallel mechanism. i According to the meaning of the kinematic solution, given the P i Coordinates, the first constraint equation group, the second constraint equation group, the third constraint equation group, the fourth constraint equation group and the fifth constraint equation group are combined to solve the terminal trajectory of the moving platform (1); the first constraint equation group, the second constraint equation group, the third constraint equation group, the fourth constraint equation group and the sixth constraint equation group are combined to solve the terminal trajectory of the moving platform (2).

5. The forward and inverse position solution method of the three-axis parallel mechanism according to claim 4 is characterized in that: The method further comprises the following steps: receiving an action instruction of the three-axis parallel mechanism, the action instruction comprising at least one of the following: translation, rotation; outputting a trajectory sequence according to the action instruction; outputting an action instruction according to the trajectory sequence; converting the P i The position vector is output to the motor servo system, so that the motor servo system controls the three-axis parallel mechanism to complete the target motion trajectory; the terminal trajectory is output to the host computer system, so that the host computer obtains the terminal reference point posture of the three-axis parallel mechanism to complete the motion control.

6. The forward and inverse position solution method of the three-axis parallel mechanism according to claim 4, characterized in that: The iterative method includes but is not limited to the Newton-Raphson numerical method.

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