Kinematics analysis method for two-degree-of-freedom planar parallel six-connecting

Abstract

The invention discloses a kinematics analysis method for a two-degree-of-freedom planar parallel six-connecting-rod mechanism. The method comprises the step of performing kinematics forward and reverse solutions on the planar parallel six-connecting-rod mechanism. For the kinematics inverse solution and the known moving platform pose, constructing a mechanism movement diagram, and according to the geometrical relationship in the mechanism diagram, dividing a triangle by taking P0P3 as a center line to gradually derive a driving pair output angle, so as to obtain a kinematics inverse solution result; and for the kinematics positive solution, a vector closed-loop method is adopted to establish a quaternary primary nonlinear equation set, a Newton-Raphson iteration method is used for solving, an iteration error is set to be smaller than or equal to e-8, an initial value is arbitrary, and the kinematics positive solution is converged to be close to a true value through finite iteration times, so that a kinematics positive solution result is obtained. The problem that when the mechanism of the type is used, the position and posture of the movable platform and the output angle of the driving pair cannot be obtained through kinematics analysis is effectively solved, and meanwhile the problems that multiple groups of solutions possibly need to be screened and the operation time is too long are solved.

Description

Technical Field

[0001] The invention relates to the field of kinematic analysis of parallel mechanisms, and in particular to a kinematic analysis method of a two-degree-of-freedom planar parallel six-link mechanism. Background Art

[0002] In modern mechanical engineering technology, kinematic analysis of various mechanisms is the key to achieving efficient, precise control and reliable operation of the mechanisms. With the continuous development of science and technology, many mechanical systems with complex structures and multiple functions are widely used in various industrial fields. The demand for mechanisms with specific functions and performance requirements is increasing, and parallel mechanisms have attracted much attention due to their potential in achieving complex motion and precise control.

[0003] Traditional kinematic analysis methods have many limitations when analyzing two-degree-of-freedom planar parallel six-bar linkages. First, for planar parallel six-bar linkages with multiple links, existing analysis methods often face the problem of large amount of calculation and low efficiency in the solution process. This not only consumes a lot of computing time, but also seriously affects production efficiency and timeliness of decision-making in actual application scenarios. Second, in actual engineering applications, when the pitch and tilt angles of the moving platform are precisely controlled, there is an urgent need for a kinematic analysis method that can quickly and accurately determine the position of the mechanism. However, the existing methods are still insufficient in this regard and it is difficult to meet the strict requirements of efficient control.

[0004] As the requirements for precision and speed in modern industrial production continue to increase, existing kinematic analysis methods often fail to meet actual needs in terms of real-time performance and reliability. In some time-sensitive application scenarios, such as automated production lines and high-speed motion control systems, kinematic analysis methods are required to provide accurate results in a very short time to ensure stable operation and efficient production of the system. At the same time, reliability is also crucial. Once the analysis results are wrong, it is very likely to cause serious production accidents and huge economic losses. In summary, the development of an efficient and accurate kinematic analysis method for two-degree-of-freedom parallel mechanisms has great practical significance. It can not only provide strong technical support for the sustainable development of the field of mechanical engineering, but also effectively promote the continuous progress and innovation of related industries. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a kinematic analysis method for a two-degree-of-freedom planar parallel six-bar mechanism that can quickly and accurately obtain the kinematic forward and inverse solutions of the parallel mechanism and can perform posture control on mechanical equipment applied to this type of structure.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: a kinematic analysis method of a two-degree-of-freedom planar parallel six-bar linkage mechanism, comprising the following steps:

[0007] S1: Analyze the motion relationship of each unit of the two-degree-of-freedom planar parallel six-bar linkage mechanism, construct a mechanism motion diagram, and establish a plane coordinate system with P0 as the origin;

[0008] S2: Given the position and posture of the moving platform, the mechanism diagram is geometrically decomposed to obtain several triangles;

[0009] S3: Analyze the known side and angle quantities of the two triangles with P0P3 as sides, and calculate their unknown side and angle quantities;

[0010] S4: continue to calculate the unknown side and angle quantities of the remaining triangles according to the calculated side and angle quantities until a kinematic inverse solution is obtained, and obtain the drive auxiliary output angles α and β based on the kinematic inverse solution results;

[0011] S5: Obtain the coordinates of each rotation sub-point in the mechanism according to the plane coordinate system, and calculate the vector represented by each connecting rod in the mechanism in the motion diagram;

[0012] S6: According to the vector closed loop method, the vector P0P3 is equal to the sum of the other two vectors, and the equation is constructed;

[0013] S7: Decompose each vector into its own x vector and y vector, and substitute them into the equation of step S6 to obtain a system of four-variable linear nonlinear equations;

[0014] S8: The Newton-Raphson iteration method is used to obtain the kinematic solution, and the dynamic platform posture parameters h and θ are obtained based on the kinematic solution results.

[0015] The beneficial effect of adopting the above technical solution is that the method provides a comprehensive kinematic forward and inverse solution method for a two-degree-of-freedom planar parallel six-bar linkage. By constructing a simple diagram of the mechanism motion, using geometric relationships and vector closed-loop methods, the posture of the mechanism and the output angle of the drive pair can be accurately solved. In the kinematic inverse solution, the triangle is divided by a specific midline and the calculation is step-by-step. The method is clear and intuitive, the calculation process is relatively simple and efficient, and the output angle of the drive pair can be quickly obtained. In the kinematic forward solution, the vector closed-loop method is used to establish a set of quaternary first-order nonlinear equations, and the Newton-Raphson iteration method is used to solve it. The method has a fast convergence speed, a small number of iterations, and a fast calculation speed. It can converge to the vicinity of the true value after a finite number of iterations to obtain accurate dynamic platform posture parameters. It effectively solves the problem that when using this type of mechanism, the posture of the dynamic platform and the output angle of the drive pair cannot be obtained through kinematic analysis. It provides a reliable analysis method for the control and use of this type of mechanism in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0017] Figure 1 is a flow chart of the method described in an embodiment of the present invention;

[0018] Figure 2 This is a planar structural diagram of a model in an embodiment of the present invention;

[0019] Figure 3 is a schematic diagram of the mechanism movement in an embodiment of the present invention;

[0020] Figure 4 is a schematic diagram of kinematic inverse solution in an embodiment of the present invention;

[0021] Figure 5 is a schematic diagram of a kinematic solution in an embodiment of the present invention;

[0022] Figure 6 is a control flow chart in an embodiment of the present invention;

[0023] Figure 7 is an overall diagram of a robot in an embodiment of the present invention;

[0024] Figure 8 It is a schematic diagram of the iterative relationship and results of the kinematics forward solution of an embodiment of the present invention. DETAILED DESCRIPTION

[0025] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0026] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0027] like Figure 1 As shown, the embodiment of the present invention discloses a kinematic analysis method for a two-degree-of-freedom planar parallel six-bar linkage mechanism, the method comprising the following steps:

[0028] S1: For a two-degree-of-freedom planar parallel six-bar linkage (such as Figure 2 Analyze the motion relationship of each unit and construct a simple motion diagram of the mechanism (as shown in Figure 3 shown);

[0029] Furthermore, in the mechanism motion diagram constructed in step S1, the motion pair categories of each point are as follows: points P1 and P2 are rotational drive pairs, points P4, P5, P6 and P7 are rotational pairs, point P3 is a rotational translation pair, and point P0 is the midpoint of the line connecting points P1 and P2.

[0030] At the same time, determine the length of each connecting rod in the mechanism: P0P1=P0P2=L=275mm, P1P7=P2P6=a=105mm, P7P5=P6P4=b=229mm, P4P5=2d=550mm.

[0031] S2: Given the position and posture of the moving platform, the mechanism diagram is geometrically decomposed to obtain several triangles, such as Figure 4 As shown;

[0032] Furthermore, in step S2, when performing kinematic inverse solution, P0P5, P1P5, P0P4, and P2P4 are connected to divide 6 triangles, namely △P0P3P5, △P0P1P5, △P1P7P5, △P0P3P4, △P0P2P4, and △P2P6P4.

[0033] S3: Analyze the known side and angle quantities of the two triangles with vector P0P3 as sides, and use formulas (1)-(4) to calculate their unknown side and angle quantities. The calculation process is as follows;

[0034] The known quantities are P0P1=P0P2=L, P1P7=P2P6=a, P7P5=P6P4=b, P4P5=2d, and P3 is the midpoint. Let P0P4=c1, P0P5=c2, P2P4=c3, P1P5=c4, ∠P4P0P3=α1, ∠P5P0P3=α2, ∠P4P2P0=β1, ∠P5P1P0=β2, ∠P4P2P6=β3, ∠P5P1P7=β4.

[0035] In △P0P3P5, the formula for solving c2 and α2 is:

[0036] c2 2 =d 2 +h 2 -2dh×cos(π / 2+θ) (1)

[0037] d 2 =c2 2 +h 2 -2c2h×cos(α2) (2)

[0038] Among them, c2 is the length of the P0P5 rod, and α2 is the radian value of the angle between the rod P5P0 and the rod P0P3.

[0039] In △P0P3P4, the formula for solving c1 and α1 is:

[0040] c1 2 =d 2 +h 2 -2dh×cos(π / 2-θ) (3)

[0041] d 2 =c1 2 +h 2 -2c1h×cos(α1) (4)

[0042] Among them, c1 is the length of the P0P4 rod, and α1 is the radian value of the angle between the rod P4P0 and the rod P0P3.

[0043] S4: Based on the calculated side angles, use formulas (5)-(12) to continue to calculate the unknown side angles of the remaining triangles until the kinematic inverse solution is obtained. Based on the kinematic inverse solution results, the drive auxiliary output angles α and β are obtained. The detailed calculation process is as follows:

[0044] Substituting c2 and α2 obtained in step S3 into △P0P1P5, the formula for solving c4 and β2 is:

[0045] c4 2 =c2 2 +L 2 -2c2L×cos(π / 2-α2) (5)

[0046] c2 2 =c4 2 +L 2 -2c4L×cos(β2) (6)

[0047] Among them, c4 is the length of the P1P5 rod, and β2 is the radian value of the angle between the rod P5P1 and the rod P1P0.

[0048] Substituting c4 into △P1P7P5, we get the formula for solving β4:

[0049] b 2 =a 2 +c4 2 -2ac4×cos(β4) (7)

[0050] Among them, β4 is the radian value of the angle between rod P5P1 and rod P1P7.

[0051] Finally, the output angle α of the driving pair P1 is obtained, and the formula is:

[0052] α=π-β2-β4 (8)

[0053] Substituting c1 and α1 obtained in step 3 into △P0P2P4, the formula for solving c3 and β1 is:

[0054] c3 2 =c1 2 +L 2 -2c1L×cos(π / 2-α1) (9)

[0055] c1 2 =c3 2 +L 2 -2c3L×cos(β1) (10)

[0056] Among them, c3 is the length of the P2P4 rod, and β1 is the radian value of the angle between the rod P4P2 and the rod P2P0.

[0057] Substituting c3 into △P2P6P4, we get the formula for solving β3:

[0058] b 2 =a 2 +c3 2 -2ac3×cos(β3) (11)

[0059] Among them, β3 is the radian value of the angle between rod P4P2 and rod P2P6.

[0060] Finally, the output angle β of the driving pair P2 is obtained, and the formula is:

[0061] β=β1+β3 (12)

[0062] S5: Establish a plane coordinate system with P0 as the origin, such as Figure 5 As shown, the coordinates of each rotation point in the mechanism are obtained according to the plane coordinate system, and the vectors represented by each connecting rod in the mechanism in the motion diagram are calculated;

[0063] In step 5, the coordinates of each point are as follows:

[0064] P0(0,0), P1(L,0), P2(-L,0), P3(0,h), P4(-d*cosθ,hd*sinθ),

[0065] P5(d*cosθ,h+d*sinθ), P6(-L+a*cosβ,a*sinβ), P7(L+a*cosα,a*sinα)

[0066] From the above coordinate values, we can obtain the vectors P0P3, P0P1, P1P7, P7P5, P5P3, P0P2, P2P6, P6P4, and P4P3 represented by each connecting rod.

[0067] S6: According to the vector closed loop method, the vector P0P3 is equal to the sum of the other two vectors, and equation (13) is constructed:

[0068] According to the vector closed loop method, the constructed equation is:

[0069] P0P1+P1P7+P7P5+P5P3 = P0P3 = P0P2+P2P6+P6P4+P4P3 (13)

[0070] S7: Decompose each vector into its own x vector and y vector, and substitute them into the equation of step S6 to obtain a system of four-variable linear nonlinear equations (14);

[0071] Specifically, decompose each vector into its own x component and y component, and substitute them into the equation in step 6 to obtain a system of quaternary linear nonlinear equations, the formula is:

[0072]

[0073] Among them, α0 is the radian value of the angle of rotation of rod P7P5 along the positive direction of x, and β0 is the radian value of the angle of rotation of rod P6P4 along the positive direction of x.

[0074] S8: The Newton-Raphson iteration method is used to obtain the kinematic solution. Based on the kinematic solution, the position parameters h and θ of the moving platform are obtained. The moving platform is a P4P5 rod.

[0075] Further, the Newton-Raphson iteration method is used to solve the nonlinear equations obtained in step S7 to obtain a kinematic solution, including the following steps:

[0076] Step S8.1: Set one side of the four equations obtained in step S7 to 0, and define the four formulas on the other side of the equations as four functions containing four unknown quantities. The four function formulas are:

[0077] f1=L+a×cos(α)+b×cos(α0)+d×cos(π+θ) (15)

[0078] f2=-L+a×cos(β)+b×cos(β0)+d×cos(θ) (16)

[0079] f3=a×sin(α)+b×sin(α0)+d×sin(π+θ)-h (17)

[0080] f4=a×sin(β)+b×sin(β0)+d×sin(θ)-h (18)

[0081] Among them, functions f1, f2, f3, and f4 all have four independent variables θ, h, β0, and α0. That is, f n =f n (θ,h,β0,α0), (n=1,2,3,4).

[0082] Step S8.2: Convert the coefficient matrix of the function described in step 8.1 into a Jacobi matrix, expressed as J=J(θ,h,β0,α0):

[0083]

[0084] Among them, each element in J(θ,h,β0,α0) is the function f of the independent variables θ,h,β0,α0. n The first-order partial derivative of (θ,h,β0,α0).

[0085] Step S8.3: Let f = (f1, f2, f3, f4) T , x = (θ, h, β0, α0) T , x (0) =(θ (0) ,h (0) , β0 (0) , α0 (0) ) T , x (k) =(θ (k) ,h (k) , β0 (k) , α0 (k) ) T .

[0086] Among them, f is a set of functional equations, x is the four variables that need to be solved, x (0) To iterate over the initial value of a given variable, x (k) is the value of the variable after k iterations.

[0087] Step S8.4: The iteration formula of the Newton-Raphson method is:

[0088] x (k+1) =x (k) -J -1 (x (k) )f(x (k) ) (20)

[0089] where x (k+1) is the variable value after iteration k+1 times, J -1 (x (k) ) is the coefficient matrix after k iterations.

[0090] Set the number of iterations k to no more than 100, △x (k) ≤e -8 , △x (k) =x (k+1) -x (k) , and finally after k iterations, each variable converges to the vicinity of the true value, thus obtaining the kinematic solution.

[0091] The above algorithm is programmed into the motion controller. Figure 6 As shown in the control flow chart, the host computer first inputs the target posture and sets the input range of the target posture (x, y, θ) to x=0, 330mm≤y=h≤240mm, 0°≤θ≤10°. The control amount of each servo motor is obtained by the kinematic inverse algorithm in the motion controller. Taking the target posture (0, 300mm, 4°) as an example, the output angles of the drive pairs P1 and P2 are obtained by kinematic inverse solution α=64.5473623169426° and β=140.448908891230°. According to the calculated output angle, the motor is started to work through position control so that the platform reaches the specified position.

[0092] At this time, the encoder in the servo feeds back the actual output of each motor and outputs the actual position and posture of the moving platform through the kinematics forward solution algorithm in the motion controller. Taking the output angle α = 70° and β = 130° as an example, the kinematics forward solution obtains the position and posture of the moving platform as (0, 311.978603856997, 2.66951323418079°). The error between the target position and the actual position is then calculated by the motion controller, and the motor control quantity is output in the next cycle, thereby eliminating the system error as much as possible and avoiding work problems caused by error accumulation.

[0093] like Figure 7 As shown, the parallel six-link mechanism is a part of a robot for replacing batteries for new energy light trucks. Figure 2 The parallel six-bar linkage shown is located at the tail of the robot. It can control the pitch angle and tilt angle of the battery platform during the process of replacing the battery. Through inverse kinematics analysis, the output angle of the drive pair can be quickly calculated according to the target posture to ensure that the platform can accurately reach the predetermined position; through forward kinematics analysis, the posture change of the platform can be monitored in real time to avoid work failure due to error accumulation. When the robot is working, the kinematic analysis method of the mechanism helps to achieve more precise control of the platform position, making it more efficient.

[0094] The invention is developed in Python language under Win11 system environment, covering the complete process from constructing the mechanism motion diagram to gradually calculating the inverse solution, establishing the coordinate system and vector calculation, and solving the positive solution using a specific method, which can comprehensively analyze the kinematic characteristics of the mechanism. The Newton-Raphson iteration method used in the kinematic positive solution has a fast convergence speed and a small number of iterations. Figure 8 It can be seen from the iterative curve shown that the variables can converge to near the true value within 10 iterations, ensuring the accuracy of the solution and the efficiency of the calculation, providing a reliable analysis method for the practical application of the two-degree-of-freedom planar parallel six-bar linkage.

[0095] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein, but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A kinematic analysis method for a two-degree-of-freedom planar parallel six-bar linkage, characterized in that The steps include: S1: Analyze the motion relationship of each unit of the two-degree-of-freedom planar parallel six-bar linkage mechanism, construct a simple diagram of the mechanism motion, and establish a plane coordinate system with P0 as the origin; S2: Given the position and posture of the moving platform, the mechanism diagram is geometrically decomposed to obtain several triangles; S3: Analyze the known side and angle quantities of the two triangles with P0P3 as sides, and calculate their unknown side and angle quantities; S4: continue to calculate the unknown side and angle quantities of the remaining triangles according to the calculated side and angle quantities until a kinematic inverse solution is obtained, and obtain the drive auxiliary output angles α and β based on the kinematic inverse solution results; S5: Obtain the coordinates of each rotation point in the mechanism according to the plane coordinate system, and calculate the vector represented by each connecting rod in the mechanism in the motion diagram; S6: According to the vector closed loop method, the vector P0P3 is equal to the sum of the other two vectors, and the equation is constructed; S7: Decompose each vector into its own x vector and y vector, and substitute them into the equation of step S6 to obtain a system of four-variable linear nonlinear equations; S8: The Newton-Raphson iteration method is used to obtain the kinematic solution, and the dynamic platform posture parameters h and θ are obtained based on the kinematic solution results.

2. The kinematic analysis method of a two-degree-of-freedom planar parallel six-bar linkage mechanism according to claim 1, characterized in that: In S1: In the constructed mechanism motion diagram, the motion pair categories of each point are as follows: points P1 and P2 are rotational drive pairs, points P4, P5, P6 and P7 are rotational pairs, point P3 is a rotational translation pair, and point P0 is the midpoint of the line connecting points P1 and P2.

3. The kinematic analysis method of a two-degree-of-freedom planar parallel six-bar linkage mechanism according to claim 1, characterized in that: In step S2: When performing inverse kinematic solution, P0P5, P1P5, P0P4, and P2P4 are connected to divide out 6 triangles, namely △P0P3P5, △P0P1P5, △P1P7P5, △P0P3P4, △P0P2P4, and △P2P6P4.

4. The kinematic analysis method of a two-degree-of-freedom planar parallel six-bar linkage mechanism according to claim 1, characterized in that: In step S3: The known quantities are P0P1=P0P2=L, P1P7=P2P6=a, P7P5=P6P4=b, P4P5=2d, and P3 is the midpoint; let P0P4=c1, P0P5=c2, P2P4=c3, P1P5=c4, ∠P4P0P3=α1, ∠P5P0P3=α2, ∠P4P2P0=β1, ∠P5P1P0=β2, ∠P4P2P6=β3, ∠P5P1P7=β4. In △P0P3P5, the formula for solving c2 and α2 is: c2 2 =d 2 +h 2 -2dh×cos(π / 2+θ) (1) d 2 =c2 2 +h 2 -2c2h×cos(α2) (2) Where c2 is the length of the P0P5 rod, and α2 is the radian value of the angle between the rod P5P0 and the rod P0P3. In △P0P3P4, the formula for solving c1 and α1 is: c1 2 =d 2 +h 2 -2dh×cos(π / 2-θ) (3) d 2 =c1 2 +h 2 -2c1h×cos(α1) (4) Among them, c1 is the length of the P0P4 rod, and α1 is the radian value of the angle between the rod P4P0 and the rod P0P3.

5. The kinematic analysis method of a two-degree-of-freedom planar parallel six-bar linkage mechanism according to claim 4, characterized in that: The S4 specifically includes the following steps: Substituting c2 and α2 obtained in step 3 into △P0P1P5, the formula for solving c4 and β2 is: c4 2 =c2 2 +L 2 -2c2L×cos(π / 2-α2) (5) c2 2 =c4 2 +L 2 -2c4L×cos(β2) (6) Among them, c4 is the length of the P1P5 rod, β2 is the radian value of the angle between the rod P5P1 and the rod P1P0; Substituting c4 into △P1P7P5, we get the formula for solving β4: b 2 =a 2 +c4 2 -2ac4×cos(β4) (7) Among them, β4 is the radian value of the angle between rod P5P1 and rod P1P7; Finally, the output angle α of the driving pair P1 is obtained, and the formula is: α＝π-β2-β4 (8) Substituting c1 and α1 obtained in step 3 into △P0P2P4, the formula for solving c3 and β1 is: c3 2 =c1 2 +L 2 -2c1L×cos(π / 2-α1) (9) c1 2 =c3 2 +L 2 -2c3L×cos(β1) (10) Among them, c3 is the length of the P2P4 rod, β1 is the radian value of the angle between the rod P4P2 and the rod P2P0; Substituting the value of c3 into △P2P6P4, the formula for solving β3 is: b 2 =a 2 +c3 2 -2ac3×cos(β3) (11) Among them, β3 is the radian value of the angle between rod P4P2 and rod P2P6. Finally, the output angle β of the driving pair P2 is obtained, and the formula is: β＝β1+β3 (12)。 6. The kinematic analysis method of a two-degree-of-freedom planar parallel six-bar linkage mechanism according to claim 5, characterized in that: The coordinates of each rotation secondary point in step S5 are as follows: P0(0,0), P1(L,0), P2(-L,0), P3(0,h), P4(-d*cosθ,hd*sinθ), P5(d*cosθ,h+d*sinθ), P6(-L+a*cosβ,a*sinβ), P7(L+a*cosα,a*sinα); From the above coordinate values, the vectors represented by each connecting rod are: P0P3, P0P1, P1P7, P7P5, P5P3, P0P2, P2P6, P6P4, and P4P3.

7. The kinematic analysis method of a two-degree-of-freedom planar parallel six-bar linkage mechanism according to claim 6, characterized in that: In step S6: According to the vector closed loop method, the constructed equation is: P0P1+P1P7+P7P5+P5P3 = P0P3 = P0P2+P2P6+P6P4+P4P3 (13).

8. The kinematic analysis method of a two-degree-of-freedom planar parallel six-bar linkage mechanism according to claim 6, characterized in that: In step S7: Decompose each vector into its x component and y component, and substitute them into the equation in step 6 to obtain a system of four-variable linear nonlinear equations, as follows: Among them, α0 is the radian value of the angle of rotation of rod P7P5 along the positive direction of x, and β0 is the radian value of the angle of rotation of rod P6P4 along the positive direction of x.

9. The kinematic analysis method of a two-degree-of-freedom planar parallel six-bar linkage mechanism according to claim 6, characterized in that: The step S8 specifically includes: S8.1: Set one side of the four equations obtained in step S7 to 0, and define the four formulas on the other side of the equations as four functions containing four unknown quantities. The four function formulas are: f1=L+a×cos(α)+b×cos(α0)+d×cos(π+θ) (15) f2=-L+a×cos(β)+b×cos(β0)+d×cos(θ) (16) f3=a×sin(α)+b×sin(α0)+d×sin(π+θ)-h (17) f4=a×sin(β)+b×sin(β0)+d×sin(θ)-h (18) Among them, functions f1, f2, f3, and f4 all have four independent variables θ, h, β0, and α0; that is, f n =f n (θ,h,β0,α0), (n=1,2,3,4); S8.2: Convert the coefficient matrix of the function described in step S8.1 into a Jacobi matrix, expressed as J=J(θ,h,β0,α0): Among them, each element in J(θ,h,β0,α0) is the function f of the independent variables θ,h,β0,α0. n The first-order partial derivative of (θ,h,β0,α0); S8.3: Let f = (f1, f2, f3, f4) T , x = (θ, h, β0, α0) T , x (0) = (θ (0) , h (0) , β0 (0) ,α0 (0) ) T ,x (k) =(θ (k) ,h (k) ,β0 (k) ,α0 (k) ) T ; Among them, f is a set of functional equations, x is the four variables that need to be solved, x (0) To iterate over the initial value of a given variable, x (k) is the variable value after k iterations; S8.4: The iterative formula for the Newton-Raphson method is: x (k+1) =x (k) -J -1 (x (k) )f(x (k) ) (20) where x (k+1) is the variable value after iteration k+1 times, J -1 (x (k) ) is the coefficient matrix after iteration k times; Set the number of iterations k to no more than 100, △x (k) ≤e -8 , △x (k) =x (k+1) -x (k) , and finally after k iterations, each variable converges to the vicinity of the true value, thus obtaining the kinematic solution.

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