Motion track solving method for metamorphic four-bar mechanism

Abstract

The invention discloses a metamorphic four-bar mechanism motion trail solving method. The method comprises the following steps: S1, establishing a three-dimensional model of a metamorphic four-bar mechanism; s2, based on the three-dimensional model of the metamorphic four-bar mechanism, motion process analysis of the metamorphic four-bar mechanism is carried out; and S3, according to the motion process analysis of the metamorphic four-bar mechanism, solving the motion trail of the metamorphic four-bar mechanism. The kinematics of the metamorphic four-bar mechanism of the mechanical leg of the robot is analyzed, the configuration of the metamorphic four-bar mechanism is described, the motion process of the metamorphic four-bar mechanism is analyzed, a mathematical model of a track curve of the metamorphic four-bar mechanism is established, and the solving method of the motion track of the metamorphic four-bar mechanism is provided. And wide application of the metamorphic four-bar mechanism in the fields of robots and the like can be realized.

Description

Technical Field

[0001] The invention belongs to the technical field of solving the motion trajectory of a four-bar mechanism, and in particular relates to a method for solving the motion trajectory of a metamorphic four-bar mechanism. Background Art

[0002] The four-bar mechanism can realize various complex motion trajectories due to its simple structure and is applied to various fields. However, once the parameters of the mechanism are determined, the motion trajectory of its end reference point is fixed and cannot be changed. After the introduction of metamorphic theory, by changing the mechanism topology during the movement, the degree of freedom and the number of components of the four-bar mechanism can be changed, and the motion trajectory of the end reference point of the mechanism can be changed, which can expand the application range of the mechanism, for example, in robots. However, in the prior art, there is still a lack of methods for analyzing the kinematics of the metamorphic four-bar mechanism of the robot's mechanical legs, and a lack of methods for solving the motion trajectory of the metamorphic four-bar mechanism. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a method for solving the motion trajectory of a metamorphic four-bar mechanism in view of the deficiencies in the above-mentioned prior art. The method analyzes the kinematics of the metamorphic four-bar mechanism of the robot mechanical leg, describes the configuration of the metamorphic four-bar mechanism, analyzes its motion process, establishes a mathematical model of the trajectory curve of the metamorphic four-bar mechanism, and proposes a method for solving the motion trajectory of the metamorphic four-bar mechanism, which is helpful to realize the expanded application of the metamorphic four-bar mechanism in the fields of robots and so on.

[0004] In order to solve the above technical problems, the technical solution adopted by the present invention is: a method for solving the motion trajectory of a variable cell four-bar mechanism, the method comprising the following steps:

[0005] Step S1, establishing a three-dimensional model of a metamorphic four-bar mechanism;

[0006] Step S2, analyzing the motion process of the metamorphic four-bar mechanism based on the three-dimensional model of the metamorphic four-bar mechanism;

[0007] Step S3: solving the motion trajectory of the metamorphic four-bar mechanism according to the motion process analysis of the metamorphic four-bar mechanism.

[0008] The above-mentioned method for solving the motion trajectory of a metamorphic four-bar mechanism, the three-dimensional model of the metamorphic four-bar mechanism established in step S1 includes a frame, an upper connecting rod, a lower connecting rod and a connecting rod, one end of the upper connecting rod and one end of the lower connecting rod are respectively hinged to the upper and lower ends of the frame, and the other end of the upper connecting rod and the other end of the lower connecting rod are respectively hinged to the upper and lower ends of the connecting rod; the hinge point between the lower connecting rod and the lower end of the frame is hinge point A, the hinge point between the upper connecting rod and the upper end of the frame is hinge point B, the hinge point between the upper connecting rod and the upper end of the connecting rod is hinge point C, and the lower connecting rod is hinged to the lower end of the frame. The hinge point between the connecting rod and the lower end of the connecting rod is hinge point D, and the hinge point A, hinge point B and hinge point C are all fixed hinge points. The frame is provided with a protruding block above the hinge point B for limiting the movement range of the connecting rod, a slide groove is provided on one side of the lower end of the connecting rod, and a motion reference point M is provided on the other side of the lower end of the connecting rod. The hinge point D is a movable hinge point that can move in the slide groove, and a support spring is provided in the slide groove, one end of the support spring is fixed at the end of the slide groove, and the other end of the support spring is connected to the movable hinge point.

[0009] In the above-mentioned method for solving the motion trajectory of a metamorphic four-bar mechanism, the specific process of analyzing the motion process of the metamorphic four-bar mechanism based on the three-dimensional model of the metamorphic four-bar mechanism in step S2 is as follows:

[0010] Step S201, dividing the motion process of the metamorphic four-bar mechanism into three stages;

[0011] Step S202: Analyze the motion trajectory of the motion reference point M on the connecting rod at each stage by using the graphical method, specifically:

[0012] Step S2021, the first stage of the movement of the metamorphic four-bar mechanism begins, the lower connecting rod rotates counterclockwise as the driving pair of the metamorphic four-bar mechanism, initially under the pressure of the support spring, the movable hinge point is pressed at the end of the slide slot, and the mechanism is a typical four-bar mechanism at this time; the movement process of the metamorphic four-bar mechanism is consistent with the movement of the typical four-bar mechanism, the connecting rod between the hinge point C and the hinge point D is taken as the driving rod, and rotates counterclockwise until the frame between the hinge point A and the hinge point B hits the block, the driving angle is defined as θ4, and the movement trajectory of point M is defined as a circular arc from M1 through M2, M3 to M4;

[0013] Step S2022, the first stage of the movement of the metamorphic four-bar mechanism ends, and the second stage of the movement begins. At this time, the upper connecting rod cannot rotate due to the action of the block, which is equivalent to being fixed to the frame. The lower connecting rod between the hinge point A and the hinge point D and the frame between the hinge point A and the hinge point B are fixed; under the action of the driving force, the connecting rod between the hinge point C and the hinge point D continues to rotate counterclockwise, the support spring is compressed, and the movement of the connecting rod changes until the hinge point C coincides with the line connecting the hinge point D and the hinge point B, and the second stage of the movement ends. The movement trajectory of point M is defined as from M5 to M 11 An arc of a circle;

[0014] Step S2023, the second stage of the movement of the metamorphic four-bar mechanism ends, and the third stage of the movement begins. The support spring is compressed to the shortest, and the connecting rod and the lower connecting rod are collinear; thereafter, the connecting rod between the hinge point A and the hinge point D and the frame between the hinge point A and the hinge point B are fixed, and the connecting rod between the hinge point C and the hinge point D continues to rotate counterclockwise, and the support spring gradually extends; the hinge point C passes over the line connecting the hinge point D and the hinge point B until the movable hinge point is pressed again at the end of the slide slot, and the third stage of the movement ends, the support spring is extended to the longest, and the movement trajectory of point M is defined as from M 12 To M 17 An arc of a circle;

[0015] Step S203: Express the motion trajectory of the motion reference point M of the metamorphic four-bar mechanism as a synthesis of the motion trajectories of three stages.

[0016] In the above-mentioned method for solving the motion trajectory of a metamorphic four-bar mechanism, the specific process of solving the motion trajectory of the metamorphic four-bar mechanism in step S3 is as follows:

[0017] Step S301, constructing a motion trajectory solving mathematical model of a metamorphic four-bar mechanism, and solving the motion trajectory curve of the first stage of the motion of the metamorphic four-bar mechanism according to the motion trajectory solving mathematical model;

[0018] Step S302, solving the motion trajectory curve of the second stage of the metamorphic four-bar mechanism motion;

[0019] Step S303, solving the motion trajectory curve of the third stage of the metamorphic four-bar mechanism motion.

[0020] In the above-mentioned method for solving the motion trajectory of a metamorphic four-bar mechanism, the specific process of constructing a motion trajectory solving mathematical model of the metamorphic four-bar mechanism in step S301, and solving the motion trajectory curve of the first stage of the motion of the metamorphic four-bar mechanism according to the motion trajectory solving mathematical model is as follows:

[0021] Step S3011, define the length of the lower connecting rod between the hinge point A and the hinge point D as r1, define the length of the frame between the hinge point A and the hinge point B as r2, define the length of the upper connecting rod between the hinge point B and the hinge point C as r3, define the length of the connecting rod between the hinge point C and the hinge point D as r4, and define the distance between the hinge point B and the motion reference point M as r5;

[0022] Step S3012, establish a global coordinate system O-XY and a local coordinate system A-xy, the local coordinate system takes the hinge point A as the origin, the coordinates of the hinge point A in the global coordinate system are (x0, y0), define θ2 as the angle between r2 and r4, define θ3 as the angle between r3 and a line parallel to r1 with the hinge point B as the starting point, define θ4 as the angle between r1 and r4, define β as the angle between r5 and a line parallel to r1 with the hinge point B as the starting point, and define α as the angle between r1 and the x-axis of the local coordinate system A-xy;

[0023] Step S3013: In the local coordinate system, θ2 is expressed as:

[0024]

[0025] Let θ3 be expressed as:

[0026]

[0027] Where A = sinθ4;

[0028] Step S3014: The coordinates of the motion reference point M in the local coordinate system A-xy are expressed as:

[0029]

[0030] Step S3015: The coordinates of the motion reference point M in the global coordinate system O-XY are expressed as:

[0031]

[0032] In the above-mentioned method for solving the motion trajectory of a metamorphic four-bar mechanism, when solving the motion trajectory curve of the second stage of the motion of the metamorphic four-bar mechanism in step S302, according to the size relationship between r2 and r4, and whether the trajectory is folded back, the solution of the second stage motion trajectory is divided into different cases, and the specific solution process is:

[0033] When r2<r4, according to the formula Calculate the size of ∠BC1D, where

[0034] Then, according to the size of ∠BC1D, determine whether there is a trajectory reentry;

[0035] When ∠BC1D<90°, it is judged that there is a trajectory reversal situation, and the motion trajectory curve solution of the second stage of the metamorphic four-bar mechanism motion is divided into two parts: the trajectory reversal part and the non-trajectory reversal part for solution;

[0036] When ∠BC1D ≥ 90°, it is judged that there is no trajectory reentry, and the solution is directly performed according to the method without trajectory reentry;

[0037] When r2 ≥ r4, first calculate the critical value r of r2 under the critical conditions BC / / AD and θ3 = 0 21 , then divide r2>r 21 and r4<r2<r 21 The motion trajectory curves of the second stage of the variable cell four-bar mechanism motion are solved in two cases.

[0038] The above-mentioned method for solving the motion trajectory of a metamorphic four-bar mechanism, when ∠BC1D<90°, divides the motion trajectory curve of the second stage of the metamorphic four-bar mechanism motion into two parts: the trajectory return part and the non-trajectory return part for solving the specific process as follows:

[0039] For the trajectory return part, such as Fig. 9 As shown, the length of r3 changes to r 3_C1 →r 3_E1 →r 3_F1 ;

[0040] For point E1, in △BE1D, DE1⊥BE1, then:

[0041]

[0042] For point F1, in △DC1F, ∠DC1F=∠DC1B; in △DBF1, ∠DBF1=π-∠DF1C1;

[0043] In △DBF1, according to the cosine theorem:

[0044]

[0045] According to formula (F6), r is calculated 3_F1 ;

[0046] The length of r3 changes from r 3_C1 →r 3_E1 and r 3_E1 →r 3_F1 The formed trajectory, the two parts of the trajectory overlap, only r is calculated 3_C1 →r 3_E1 The specific process is:

[0047] r3_C1 →r 3_E1 Divide into n1 equal parts, and take any point C 11 ,like Fig. 9 As shown;

[0048] In △DC 11 In B, according to the cosine theorem:

[0049]

[0050] Since BG1 / / AD, ∠DBG1=∠ADB, so ∠G1 B1C1=∠DB1C1-∠D, let θ3=∠G1BC, then we get:

[0051] θ3=∠DBC 11 -∠DBG1 (F8)

[0052] Calculate θ3 corresponding to each of the n1 equal parts, and get the set of motion trajectories of point M as follows:

[0053] For the untrajectory return part, such as Fig. 9 As shown, the length of r3 changes to r 3_F1 →r 3_H1 ; Divided into two parts according to θ3>0 and θ3<0;

[0054] When θ3=0, the length of BG1 / / AD,r is r 3_G1 ;

[0055] For point G1, in △BDG1, according to the cosine theorem:

[0056]

[0057] Find the root and get r 3_G1 ;

[0058] For point H1, when r4 and l BD When collinear, r3 has the shortest length r 3_H1 , then:

[0059] r 3_H1 = l BD -r4 (F10)

[0060] When θ3>0, r 3_F1 →r 3_G1 Divide into n2 equal parts, take C 12 For any point, such as Fig.10 As shown;

[0061] In △BC 12 In D, by the law of cosines, we get:

[0062]

[0063] In △ABD, r1, r2 and l BD As is known, θ5 is expressed as:

[0064]

[0065] From AD / / BG, we get:

[0066] θ3=(θ8-θ5)>0 (F13)

[0067] Calculate θ3 corresponding to each of the n2 equal parts, and get the motion trajectory of point M as follows:

[0068] When θ3<0, r 3_G1 →r 3_H1 Divide into n3 equal parts, take C 13 For any point, such as Fig.11 As shown;

[0069] Using the cosine theorem, we can get θ5 and θ8, then θ3=(θ8-θ5)<0. Calculate the θ3 corresponding to each of the n3 equal parts, and get the motion trajectory of point M as follows:

[0070] The motion trajectory of the moving reference point M when there is a trajectory reversal is expressed as:

[0071]

[0072] When ∠BC1D≥90°, the solution is performed according to the solution method of the non-trajectory return part. When θ3>0, r 3_F1 →r 3_G 2 Divide it into n4 equal parts, and the motion trajectory of point M is When θ3<0, r 3_G2 →r 3_H 2 Divide into n5 equal parts, and get the motion trajectory of point M as follows: The motion trajectory of the moving reference point M is expressed as:

[0073]

[0074] The above-mentioned method for solving the motion trajectory of a variable cell four-bar mechanism, the distribution r2>r 21 and r4<r2<r 21 The specific method for solving the motion trajectory curve of the second stage of the variable cell four-bar mechanism motion in two cases is:

[0075] When r2>r 21 When the length of r3 changes from r3→r3_H2 , r3→r 3_H2 Divide into n6 equal parts, take C 16 For any one of them;

[0076] In △BC 16 In D, the law of cosines gives:

[0077]

[0078] In △ABD, the law of cosines gives:

[0079]

[0080] θ3 is calculated according to θ3=θ8-θ5;

[0081] Calculate the θ3 corresponding to each of the n6 equal parts, and get the set of motion trajectories of point M as follows:

[0082] When r4<r2<r 21 When r2<r4 is used, the solution is performed according to the solution method when r2<r4. First, it is determined whether there is a trajectory reversal. When it is determined that there is a trajectory reversal, the motion trajectory curve solution of the second stage of the metamorphic four-bar mechanism movement is divided into two parts: the trajectory reversal part and the non-trajectory reversal part for solution; when it is determined that there is no trajectory reversal, the motion trajectory curve solution of the second stage of the metamorphic four-bar mechanism movement is solved according to the non-trajectory reversal part;

[0083] When it is determined that there is a trajectory return, the length of the trajectory return portion r3 changes to r3→r 3_E3 →r 3_F3 , r3→r 3_E3 Divide into n7 equal parts, and get the set of motion trajectories of point M as follows: The length of the untrajectory return portion r3 changes to r 3_F3 →r 3_H3 , r 3_F3 →r 3_H3 Divide into n8 equal parts, and get the set of motion trajectories of point M as follows: When there is a trajectory reversal, the motion trajectory set of point M is expressed as

[0084] When it is determined that there is no trajectory reversal, the length of r3 changes to r3→r 3_H3 ; r3→r 3_H3 Divide into n9 equal parts, and get the set of motion trajectories of point M as follows:

[0085] In the above-mentioned method for solving the motion trajectory of a metamorphic four-bar mechanism, when solving the motion trajectory curve of the third stage of the motion of the metamorphic four-bar mechanism in step S303, the solution is performed based on the symmetry between the third stage motion trajectory and the second stage motion trajectory about the straight line BD.

[0086] Compared with the prior art, the present invention has the following advantages: the present invention analyzes the kinematics of the metamorphic four-bar mechanism of the robot mechanical leg, describes the configuration of the metamorphic four-bar mechanism, analyzes its motion process, establishes a mathematical model of the trajectory curve of the metamorphic four-bar mechanism, and proposes a method for solving the motion trajectory of the metamorphic four-bar mechanism, which is helpful to realize the expanded application of the metamorphic four-bar mechanism in the fields of robots and so on.

[0087] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 is a flowchart of the method of the present invention;

[0089] Figure 2A A three-dimensional model of the metamorphic four-bar mechanical leg mechanism analyzed by the present invention;

[0090] Figure 2B A schematic diagram of the metamorphosis kinematic pair analyzed by the present invention;

[0091] Figure 3A It is a schematic diagram of the initial moment of the first stage of the metamorphic four-bar mechanism of the present invention;

[0092] Figure 3B It is a schematic diagram of the initial moment of the second stage of the metamorphic four-bar mechanism of the present invention;

[0093] Figure 3C It is a schematic diagram of the initial moment of the third stage of the metamorphic four-bar mechanism of the present invention;

[0094] Figure 3D It is a schematic diagram of the end time of the third stage of the metamorphic four-bar mechanism of the present invention;

[0095] Figure 4A It is a schematic diagram of the first stage of the movement of the metamorphic four-bar mechanism of the present invention;

[0096] Figure 4B It is a schematic diagram of the second stage of the metamorphic four-bar mechanism of the present invention;

[0097] Figure 4C It is a schematic diagram of the third stage of the movement of the metamorphic four-bar mechanism of the present invention;

[0098] Figure 5 It is a schematic diagram of the overall motion trajectory of the metamorphic four-bar mechanism of the present invention;

[0099] Figure 6 This is a schematic diagram of the metamorphic four-bar mechanical leg mechanism of the present invention;

[0100] Figure 7 It is a schematic diagram of the trajectory return situation of the present invention;

[0101] Figure 8 This is a flow chart for solving the problem of r2<r4 in the second stage of the present invention;

[0102] Fig. 9 This is a schematic diagram of the second stage of the present invention, r2<r4 and the trajectory return situation;

[0103] Fig.10 The second stage of the present invention is r3, the length of the rod is from r 3_F1 →r 3_G 1 Schematic diagram;

[0104] Fig.11 The second stage of the present invention is r3, the length of the rod is from r 3_G1 →r 3_H 1 Schematic diagram;

[0105] Fig.12 This is a flow chart for solving the problem of r2≥r4 in the second stage of the present invention;

[0106] Fig.13 This is a schematic diagram of the second stage of the present invention when θ3 < 0;

[0107] Fig.14 This is the second stage of the present invention r2>r 21 Schematic diagram of the situation;

[0108] Fig.15 Schematic diagram of the effect of the change of r1 on the motion trajectory of the mechanism in a specific embodiment of the present invention.

[0109] Description of reference numerals:

[0110] 1—frame; 2—upper connecting rod; 3—connecting rod;

[0111] 4—Lower connecting rod; 5—Movable hinge point; 6—Support spring. DETAILED DESCRIPTION

[0112] like Figure 1 As shown, the method for solving the motion trajectory of the metamorphic four-bar mechanism of the present invention comprises the following steps:

[0113] Step S1, establishing a three-dimensional model of a metamorphic four-bar mechanism;

[0114] Step S2, analyzing the motion process of the metamorphic four-bar mechanism based on the three-dimensional model of the metamorphic four-bar mechanism;

[0115] Step S3: solving the motion trajectory of the metamorphic four-bar mechanism according to the motion process analysis of the metamorphic four-bar mechanism.

[0116] In this embodiment, Figure 2A and Figure 2B As shown, the three-dimensional model of the metamorphic four-bar mechanism established in step S1 includes a frame 1, an upper connecting rod 2, a lower connecting rod 4 and a connecting rod 3, one end of the upper connecting rod 2 and one end of the lower connecting rod 4 are respectively hinged to the upper and lower ends of the frame 1, and the other end of the upper connecting rod 2 and the other end of the lower connecting rod 4 are respectively hinged to the upper and lower ends of the connecting rod 3; the hinge point between the lower connecting rod 4 and the lower end of the frame 1 is hinge point A, the hinge point between the upper connecting rod 2 and the upper end of the frame 1 is hinge point B, the hinge point between the upper connecting rod 2 and the upper end of the connecting rod 3 is hinge point C, and the lower connecting rod 4 and the connecting rod 3 are respectively hinged to the upper and lower ends of the frame 1. The hinge point at the lower end of the rod 3 is the hinge point D, and the hinge point A, hinge point B and hinge point C are all fixed hinge points. The frame 1 is provided with a protruding stopper located above the hinge point B for limiting the movement range of the connecting rod 2. A slide groove is provided on one side of the lower end of the connecting rod 3, and a movement reference point M is provided on the other side of the lower end of the connecting rod 3. The hinge point D is a movable hinge point 5 that can move in the slide groove, and a support spring 6 is provided in the slide groove, one end of the support spring 6 is fixed at the end of the slide groove, and the other end of the support spring 6 is connected to the movable hinge point 5.

[0117] When the movable hinge point 5 moves in the slide groove, the metamorphic motion pair has two degrees of freedom, movement and rotation, which is equivalent to a high pair; when the movable hinge point 5 is pushed against one end of the slide groove under the action of the support spring 6 and cannot move, the metamorphic motion pair only has a rotational movement pair.

[0118] In this embodiment, the specific process of performing the motion process analysis of the metamorphic four-bar mechanism based on the three-dimensional model of the metamorphic four-bar mechanism in step S2 is as follows:

[0119] Step S201, dividing the motion process of the metamorphic four-bar mechanism into three stages;

[0120] Step S202: Analyze the motion trajectory of the motion reference point M on the connecting rod 3 at each stage by using the graphical method, specifically:

[0121] Step S2021: Figure 3A As shown, the first stage of the movement of the metamorphic four-bar mechanism begins, the lower connecting rod 4 rotates counterclockwise as the driving pair of the metamorphic four-bar mechanism, and initially under the pressure of the support spring 6, the movable hinge point 5 (hinge point D) is pressed at the end of the slide slot, and the mechanism is a typical four-bar mechanism; Figure 4AAs shown, the motion process of the metamorphic four-bar mechanism is consistent with that of the typical four-bar mechanism. The connecting rod 3 between the hinge point C and the hinge point D is taken as the driving rod, and rotated counterclockwise until the frame 1 between the hinge point A and the hinge point B hits the block. Figure 4A In the solid circle, the driving angle is defined as θ4, and the motion trajectory of point M is defined as an arc from M1 through M2, M3 to M4;

[0122] Step S2022: Figure 3B As shown, the first stage of the movement of the metamorphic four-bar mechanism ends and the second stage of the movement begins. At this time, the upper connecting rod 2 cannot rotate due to the action of the block, which is equivalent to being fixed to the frame 1. The lower connecting rod 4 between the hinge point A and the hinge point D and the frame 1 between the hinge point A and the hinge point B are fixed; Figure 4B As shown in FIG. 1 , under the action of the driving force, the connecting rod 3 between the hinge point C and the hinge point D continues to rotate counterclockwise, the support spring 6 is compressed, and the movement of the connecting rod 3 changes until the hinge point C coincides with the line connecting the hinge point D and the hinge point B. The second stage of the movement ends, and the movement trajectory of point M is defined as from M5 to M 11 An arc of a circle;

[0123] Step S2023: Figure 3C As shown, the second stage of the metamorphic four-bar mechanism movement ends and the third stage of the movement begins. The support spring 6 is compressed to the shortest, and the connecting rod 3 and the lower connecting rod 4 are collinear. After that, the connecting rod 3 between the hinge point A and the hinge point D and the frame 1 between the hinge point A and the hinge point B are fixed, and the connecting rod 3 between the hinge point C and the hinge point D continues to rotate counterclockwise, and the support spring 6 gradually extends. Figure 4C As shown, the hinge point C passes over the line connecting the hinge point D and the hinge point B until the movable hinge point 5 (hinge point D) is pressed again at the end of the slide slot, the third stage of the movement ends, the support spring 6 is stretched to its maximum, and the movement trajectory of point M is defined as the movement from M to 12 To M 17 An arc of a circle;

[0124] The schematic diagram of the metamorphic four-bar mechanism at the end of the third stage of motion is as follows: Figure 3D As shown;

[0125] Step S203: The motion trajectory of the motion reference point M of the metamorphic four-bar mechanism is represented as a synthesis of the motion trajectories of the three stages, such as Figure 5 shown.

[0126] In this embodiment, the specific process of solving the motion trajectory of the metamorphic four-bar mechanism in step S3 according to the motion process analysis of the metamorphic four-bar mechanism is as follows:

[0127] Step S301, constructing a motion trajectory solving mathematical model of a metamorphic four-bar mechanism, and solving the motion trajectory curve of the first stage of the motion of the metamorphic four-bar mechanism according to the motion trajectory solving mathematical model;

[0128] Step S302, solving the motion trajectory curve of the second stage of the metamorphic four-bar mechanism motion;

[0129] Step S303, solving the motion trajectory curve of the third stage of the metamorphic four-bar mechanism motion.

[0130] In this embodiment, the specific process of constructing the motion trajectory solving mathematical model of the metamorphic four-bar mechanism in step S301, and solving the motion trajectory curve of the first stage of the motion of the metamorphic four-bar mechanism according to the motion trajectory solving mathematical model is as follows:

[0131] Step S3011: Figure 6 As shown, the length of the lower connecting rod 4 between the hinge point A and the hinge point D is defined as r1, the length of the frame 1 between the hinge point A and the hinge point B is defined as r2, the length of the upper connecting rod 2 between the hinge point B and the hinge point C is defined as r3, the length of the connecting rod 3 between the hinge point C and the hinge point D is defined as r4, and the distance between the hinge point B and the motion reference point M is defined as r5;

[0132] Step S3012: Figure 6 As shown, a global coordinate system O-XY and a local coordinate system A-xy are established. The local coordinate system takes the hinge point A as the origin. The coordinates of the hinge point A in the global coordinate system are (x0, y0). θ2 is defined as the angle between r2 and r4. θ3 is defined as the angle between r3 and a line parallel to r1 starting from the hinge point B. θ4 is defined as the angle between r1 and r4. β is defined as the angle between r5 and a line parallel to r1 starting from the hinge point B. α is defined as the angle between r1 and the x-axis of the local coordinate system A-xy.

[0133] Step S3013: In the local coordinate system, θ2 is expressed as:

[0134]

[0135] Let θ3 be expressed as:

[0136]

[0137] Where A = sinθ4;

[0138] Step S3014: The coordinates of the motion reference point M in the local coordinate system A-xy are expressed as:

[0139]

[0140] Step S3015: The coordinates of the motion reference point M in the global coordinate system O-XY are expressed as:

[0141]

[0142] To obtain the motion trajectory of the metamorphic four-bar mechanism, it is necessary to perform a step-by-step analysis based on the division of the previous motion stages, obtain the changes of θ2 and θ4 in the local coordinate system of the mechanism in each motion stage, and then obtain the coordinates of point M in the local coordinate system, and obtain the motion trajectory of point M through coordinate transformation. In the first stage, the length of the r3 rod remains unchanged, and the overall mechanism is a typical four-bar mechanism.

[0143] In the initial process of the second stage of the movement, the mechanism will experience a "trajectory reversal" situation, such as Figure 7 As shown in the figure, since the length of r3 gradually decreases from BC1 to BC2, here, r 3_C1 Indicates BC1, r 3_E1 represents BE1, and so on. As r4 rotates, r3 is gradually compressed. 3_C1 After r 3_E1 Reduce to r 3_F1 When r3 continues from r 3_F1 After r 3_E2 Reduce to r 3_C2 When the arc is turned back, it returns to point M2 along this trajectory. This arc is called the "trajectory return". Figure 7 It can be seen that at the beginning of the second stage of the mechanism movement, ∠BC1D<90°, at this time the mechanism trajectory point is at M2, and when the mechanism trajectory point reaches point M4, BC1⊥DF1. Therefore, when the mechanism is at the beginning of the second stage of movement, ∠BC1D≥90°, the mechanism will not have a "trajectory reversal" situation.

[0144] In this embodiment, when solving the motion trajectory curve of the second stage of the metamorphic four-bar mechanism motion in step S302, the solution of the second stage motion trajectory is divided into different cases according to the size relationship between r2 and r4 and whether the trajectory is retraced. The specific solution process is as follows:

[0145] When r2<r4, the solution process is as follows Figure 8 As shown, according to the formula Calculate the size of ∠BC1D, where

[0146] Then, according to the size of ∠BC1D, determine whether there is a trajectory reentry;

[0147] When ∠BC1D<90°, it is judged that there is a trajectory reversal situation, and the motion trajectory curve solution of the second stage of the metamorphic four-bar mechanism motion is divided into two parts: the trajectory reversal part and the non-trajectory reversal part for solution;

[0148] When ∠BC1D ≥ 90°, it is judged that there is no trajectory reentry, and the solution is directly performed according to the method without trajectory reentry;

[0149] When r2≥r4, the solution process is as follows Fig.12 As shown, first calculate the critical value r of r2 under the critical conditions BC / / AD and θ3 = 0 21 , then divide r2>r 21 and r4<r2<r 21 The motion trajectory curves of the second stage of the variable cell four-bar mechanism motion are solved in two cases.

[0150] When r2 changes within a certain range, θ3 < 0, and point G does not exist, so the value of the rod length r2 at this time should be determined first. The critical value r2 at this time is calculated by the critical conditions BC / / AD and θ3 = 0. 21 .like Fig.13 As shown;

[0151] In △BCD, according to the cosine theorem:

[0152]

[0153] And ∠ADB=∠DBC, in △ADB, we get:

[0154]

[0155] According to r 21 The relationship between the size of r2 can be divided into two cases: r2>r 21 and r4<r2<r 21 .

[0156] In this embodiment, when ∠BC1D<90°, the specific process of solving the motion trajectory curve of the second stage of the metamorphic four-bar mechanism motion is divided into two parts: the trajectory return part and the non-trajectory return part.

[0157] For the trajectory return part, such as Fig. 9 As shown, the length of r3 changes to r 3_C1 →r 3_E1 →r 3_F1 ;

[0158] For point E1, in △BE1D, DE1⊥BE1, then:

[0159]

[0160] This determines the location of point E1;

[0161] For point F1, in △DC1F, ∠DC1F=∠DC1B; in △DBF1, ∠DBF1=π-∠DF1C1;

[0162] In △DBF1, according to the cosine theorem:

[0163]

[0164] According to the formula (F6, calculate r 3_F1 ;

[0165] This determines the position of point F1;

[0166] The length of r3 changes from r 3_C1 →r 3_E1 and r 3_E1 →r 3_F1 The formed trajectory, the two parts of the trajectory overlap, only r is calculated 3_C1 →r 3_E1 The specific process is:

[0167] r 3_C1 →r 3_E1 Divide into n1 equal parts, and take any point C 11 ,like Fig. 9 As shown;

[0168] In △DC 11 In B, according to the cosine theorem:

[0169]

[0170] Since BG1 / / AD, ∠DBG1=∠ADB, so ∠G1 B1C1=∠DB1C1-∠D, let θ3=∠G1BC, then we get:

[0171] θ3=∠DBC 11 -∠DBG1 (F8)

[0172] Calculate the θ3 corresponding to each of the n1 equal parts, and get the set of motion trajectories of point M as [M 21 ] 2×n1 ;

[0173] In specific implementation, θ2 is known and fixed at the beginning of the second stage;

[0174] For the untrajectory return part, such as Fig. 9 As shown, the length of r3 changes to r 3_F1 →r 3_H1 ; Divided into two parts according to θ3>0 and θ3<0;

[0175] When θ3=0, the length of BG1 / / AD,r is r 3_G1 ;

[0176] For point G1, in △BDG1, according to the cosine theorem:

[0177]

[0178] Find the root and get r 3_G1 ;

[0179] For point H1, when r4 and l BD When collinear, r3 has the shortest length r 3_H1 , then:

[0180] r 3_H1 = l BD -r4 (F10)

[0181] When θ3>0, r 3_F1 →r 3_G1 Divide into n2 equal parts, take C 12 For any point, such as Fig.10 As shown;

[0182] In △BC 12 In D, by the law of cosines, we get:

[0183]

[0184] In △ABD, r1, r2 and l BD As is known, θ5 is expressed as:

[0185]

[0186] From AD / / BG, we get:

[0187] θ3=(θ8-θ5)>0 (F13)

[0188] Calculate θ3 corresponding to each of the n2 equal parts, and get the motion trajectory of point M as follows:

[0189] In specific implementation, θ2 is known and fixed at the beginning of the second stage;

[0190] When θ3<0, r 3_G1 →r 3_H1 Divide into n3 equal parts, take C 13 For any point, such as Fig.11 As shown;

[0191] Using the cosine theorem, we can get θ5 and θ8, then θ3=(θ8-θ5)<0. Calculate the θ3 corresponding to each of the n3 equal parts, and get the motion trajectory of point M as follows:

[0192] The motion trajectory of the moving reference point M when there is a trajectory reversal is expressed as:

[0193]

[0194] When ∠BC1D≥90°, the solution is performed according to the solution method of the non-trajectory return part. When θ3>0, r 3_F1 →r 3_G 2 Divide it into n4 equal parts, and the motion trajectory of point M is When θ3<0, r 3_G2 →r 3_H 2 Divide into n5 equal parts, and get the motion trajectory of point M as follows: The motion trajectory of the moving reference point M is expressed as:

[0195]

[0196] In this embodiment, the ratio r2>r 21 and r4<r2<r 21 The specific method for solving the motion trajectory curve of the second stage of the variable cell four-bar mechanism motion in two cases is:

[0197] When r2>r 21 When Fig.14 As shown, point G cannot intersect with, that is, point G does not exist, and the length of r3 changes from r3→r 3_H2 , r3→r 3_H2 Divide into n6 equal parts, take C 16 For any one of them;

[0198] In △BC 16 In D, the law of cosines gives:

[0199]

[0200] In △ABD, the law of cosines gives:

[0201]

[0202] θ3 is calculated according to θ3=θ8-θ5;

[0203] Calculate the θ3 corresponding to each of the n6 equal parts, and get the set of motion trajectories of point M as follows:

[0204] When r4<r2<r 21When r2<r4 is used, the solution is performed according to the solution method when r2<r4. First, it is determined whether there is a trajectory reversal. When it is determined that there is a trajectory reversal, the motion trajectory curve solution of the second stage of the metamorphic four-bar mechanism movement is divided into two parts: the trajectory reversal part and the non-trajectory reversal part for solution; when it is determined that there is no trajectory reversal, the motion trajectory curve solution of the second stage of the metamorphic four-bar mechanism movement is solved according to the non-trajectory reversal part;

[0205] When it is determined that there is a trajectory return, the length of the trajectory return portion r3 changes to r3→r 3_E3 →r 3_F3 , r3→r 3_E3 Divide into n7 equal parts, and get the set of motion trajectories of point M as follows: The length of the untrajectory return portion r3 changes to r 3_F3 →r 3_H3 , r 3_F3 →r 3_H3 Divide into n8 equal parts, and get the set of motion trajectories of point M as follows: When there is a trajectory reversal, the motion trajectory set of point M is expressed as

[0206] When it is determined that there is no trajectory reversal, the length of r3 changes to r3→r 3_H3 ; r3→r 3_H3 Divide into n9 equal parts, and get the set of motion trajectories of point M as follows:

[0207] In summary, according to the length of each rod, the trajectory M2 of the second stage of the mechanism movement can be obtained through calculation.

[0208] In this embodiment, when solving the motion trajectory curve of the third stage of the metamorphic four-bar mechanism motion in step S303, the solution is performed based on the symmetry between the motion trajectory of the third stage and the motion trajectory of the second stage about the straight line BD.

[0209] After the second stage motion trajectory is solved, the third stage motion trajectory is also easy to obtain. The third stage trajectory is taken as M3; the first stage mechanism motion trajectory is taken as M1, then the mechanism motion trajectory can be expressed as:

[0210] M=[M1 M2 M3] 2×n .

[0211] From the previous analysis, we can see that with a single driving hinge, the movement of the mechanism has a three-stage trajectory; take r1 = 100mm, r2 = 100mm, r3 = 122mm, r4 = 74mm, r5 = 120mm, x0 = 50mm, y0 = 200mm, α = 20°, β = -5°. According to the previous kinematic analysis, using MATLAB programming, we can get the movement trajectory when the parameters of a single mechanism change. When r1 changes in the interval [60, 120], the movement trajectory of the mechanism changes as follows: Fig.15 shown.

[0212] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any way. Any simple modification, change and equivalent structural change made to the above embodiment based on the technical essence of the present invention still falls within the protection scope of the technical solution of the present invention.

Claims

1. A method for solving the motion trajectory of a variable cell four-bar mechanism, characterized in that: The method comprises the following steps: Step S1, establishing a three-dimensional model of a metamorphic four-bar mechanism; Step S2, analyzing the motion process of the metamorphic four-bar mechanism based on the three-dimensional model of the metamorphic four-bar mechanism; Step S3, solving the motion trajectory of the metamorphic four-bar mechanism according to the motion process analysis of the metamorphic four-bar mechanism.

2. A method for solving the motion trajectory of a metamorphic four-bar mechanism according to claim 1, characterized in that: The three-dimensional model of the metamorphic four-bar mechanism established in step S1 comprises a frame (1), an upper connecting rod (2), a lower connecting rod (4) and a connecting rod (3), wherein one end of the upper connecting rod (2) and one end of the lower connecting rod (4) are respectively hinged to the upper and lower ends of the frame (1), and the other end of the upper connecting rod (2) and the other end of the lower connecting rod (4) are respectively hinged to the upper and lower ends of the connecting rod (3); the hinge point between the lower connecting rod (4) and the lower end of the frame (1) is hinge point A, the hinge point between the upper connecting rod (2) and the upper end of the frame (1) is hinge point B, the hinge point between the upper connecting rod (2) and the upper end of the connecting rod (3) is hinge point C, and the hinge point between the lower connecting rod (4) and the lower end of the frame (1) is hinge point A. The hinge point between the rod (4) and the lower end of the connecting rod (3) is hinge point D, and the hinge point A, hinge point B and hinge point C are all fixed hinge points. The frame (1) is provided with a protruding stopper located above hinge point B for limiting the movement range of the connecting rod (2). A slide groove is provided on one side of the lower end of the connecting rod (3), and a movement reference point M is provided on the other side of the lower end of the connecting rod (3). The hinge point D is a movable hinge point (5) that can move in the slide groove. A support spring (6) is provided in the slide groove, and one end of the support spring (6) is fixed to the end of the slide groove, and the other end of the support spring (6) is connected to the movable hinge point (5).

3. A method for solving the motion trajectory of a metamorphic four-bar mechanism according to claim 2, characterized in that: The specific process of analyzing the motion process of the metamorphic four-bar mechanism based on the three-dimensional model of the metamorphic four-bar mechanism in step S2 is as follows: Step S201, dividing the motion process of the metamorphic four-bar mechanism into three stages; Step S202: Analyze the motion trajectory of the motion reference point M on the connecting rod (3) at each stage by using a graphical method, specifically: Step S2021, the first stage of the movement of the metamorphic four-bar mechanism begins, the lower connecting rod (4) rotates counterclockwise as the driving pair of the metamorphic four-bar mechanism, initially under the pressure of the support spring (6), the movable hinge point (5) is pressed at the end of the slide slot, and the mechanism is a typical four-bar mechanism; the movement process of the metamorphic four-bar mechanism is consistent with the movement of the typical four-bar mechanism, the connecting rod (3) between the hinge point C and the hinge point D is taken as the driving rod, and rotates counterclockwise until the frame (1) between the hinge point A and the hinge point B hits the block, the driving angle is defined as θ4, and the movement trajectory of point M is defined as a circular arc from M1 through M2, M3 to M4; Step S2022, the first stage of the movement of the metamorphic four-bar mechanism ends, and the second stage of the movement begins. At this time, the upper connecting rod (2) cannot rotate due to the action of the block, which is equivalent to being fixed to the frame (1). The lower connecting rod (4) between the hinge point A and the hinge point D and the frame (1) between the hinge point A and the hinge point B are fixed; under the action of the driving force, the connecting rod (3) between the hinge point C and the hinge point D continues to rotate counterclockwise, the support spring (6) is compressed, and the movement of the connecting rod (3) changes until the hinge point C coincides with the line connecting the hinge point D and the hinge point B, and the second stage of the movement ends. The movement trajectory of point M is defined as from M5 to M 11 An arc of a circle; Step S2023, the second stage of the movement of the metamorphic four-bar mechanism ends, and the third stage of the movement begins. The support spring (6) is compressed to the shortest, and the connecting rod (3) and the lower connecting rod (4) are collinear; thereafter, the connecting rod (3) between the hinge point A and the hinge point D and the frame (1) between the hinge point A and the hinge point B remain stationary, and the connecting rod (3) between the hinge point C and the hinge point D continues to rotate counterclockwise, and the support spring (6) gradually extends; the hinge point C passes over the line connecting the hinge point D and the hinge point B until the movable hinge point (5) is pressed again at the end of the slide slot, and the third stage of the movement ends. The support spring (6) is extended to the longest, and the movement trajectory of point M is defined as from M 12 To M 17 An arc of a circle; Step S203: Express the motion trajectory of the motion reference point M of the metamorphic four-bar mechanism as a synthesis of the motion trajectories of three stages.

4. A method for solving the motion trajectory of a metamorphic four-bar mechanism according to claim 3, characterized in that: In step S3, according to the motion process analysis of the metamorphic four-bar mechanism, the specific process of solving the motion trajectory of the metamorphic four-bar mechanism is as follows: Step S301, constructing a motion trajectory solving mathematical model of a metamorphic four-bar mechanism, and solving the motion trajectory curve of the first stage of the motion of the metamorphic four-bar mechanism according to the motion trajectory solving mathematical model; Step S302, solving the motion trajectory curve of the second stage of the metamorphic four-bar mechanism motion; Step S303, solving the motion trajectory curve of the third stage of the metamorphic four-bar mechanism motion.

5. A method for solving the motion trajectory of a metamorphic four-bar mechanism according to claim 4, characterized in that: The specific process of constructing the motion trajectory solving mathematical model of the metamorphic four-bar mechanism in step S301 and solving the motion trajectory curve of the first stage of the motion of the metamorphic four-bar mechanism according to the motion trajectory solving mathematical model is as follows: Step S3011, define the length of the lower connecting rod (4) between the hinge point A and the hinge point D as r1, define the length of the frame (1) between the hinge point A and the hinge point B as r2, define the length of the upper connecting rod (2) between the hinge point B and the hinge point C as r3, define the length of the connecting rod (3) between the hinge point C and the hinge point D as r4, and define the distance between the hinge point B and the motion reference point M as r5; Step S3012, establish a global coordinate system O-XY and a local coordinate system A-xy, the local coordinate system takes the hinge point A as the origin, the coordinates of the hinge point A in the global coordinate system are (x0, y0), define θ2 as the angle between r2 and r4, define θ3 as the angle between r3 and a line parallel to r1 with the hinge point B as the starting point, define θ4 as the angle between r1 and r4, define β as the angle between r5 and a line parallel to r1 with the hinge point B as the starting point, and define α as the angle between r1 and the x-axis of the local coordinate system A-xy; Step S3013: In the local coordinate system, θ2 is expressed as: Let θ3 be expressed as: Where A = sinθ4; Step S3014: The coordinates of the motion reference point M in the local coordinate system A-xy are expressed as: Step S3015: The coordinates of the motion reference point M in the global coordinate system O-XY are expressed as:

6. A method for solving the motion trajectory of a metamorphic four-bar mechanism according to claim 4, characterized in that: When solving the motion trajectory curve of the second stage of the metamorphic four-bar mechanism motion in step S302, according to the size relationship between r2 and r4, and whether the trajectory is folded back, the solution of the second stage motion trajectory is divided into different cases, and the specific solution process is: When r2<r4, according to the formula Calculate the size of ∠BC1D, where Then, according to the size of ∠BC1D, determine whether there is a trajectory reentry; When ∠BC1D<90°, it is judged that there is a trajectory reversal situation, and the motion trajectory curve solution of the second stage of the metamorphic four-bar mechanism motion is divided into two parts: the trajectory reversal part and the non-trajectory reversal part for solution; When ∠BC1D ≥ 90°, it is judged that there is no trajectory reentry, and the solution is directly performed according to the method without trajectory reentry; When r2 ≥ r4, first calculate the critical value r of r2 under the critical conditions BC / / AD and θ3 = 0 21 , then divide r2>r 21 and r4<r2<r 21 The motion trajectory curves of the second stage of the variable cell four-bar mechanism motion are solved in two cases.

7. A method for solving the motion trajectory of a metamorphic four-bar mechanism according to claim 6, characterized in that: When ∠BC1D<90°, the specific process of solving the motion trajectory curve of the second stage of the metamorphic four-bar mechanism motion is divided into two parts: the trajectory return part and the non-trajectory return part. For the return portion of the track, as shown in Figure 9, the length of r3 changes to r 3_C1 →r 3_E1 →r 3_F1 ; For point E1, in △BE1D, DE1⊥BE1, then: For point F1, in △DC1F, ∠DC1F=∠DC1B; in △DBF1, ∠DBF1=π-∠DF1C1; In △DBF1, according to the cosine theorem: According to formula (F6), r is calculated 3_F1 ; The length of r3 changes from r 3_C1 →r 3_E1 and r 3_E1 →r 3_F1 The formed trajectory, the two parts of the trajectory overlap, only r is calculated 3_C1 →r 3_E1 The specific process is: r 3_C1 →r 3_E1 Divide into n1 equal parts, and take any point C 11 , as shown in Figure 9; In △DC 11 In B, according to the cosine theorem: Since BG1 / / AD, ∠DBG1=∠ADB, so ∠G1B1C1=∠DB1C1-∠D, let θ3=∠G1BC, then we get: θ3=∠DBC 11 -∠DBG1 (F8) Calculate θ3 corresponding to each of the n1 equal parts, and get the set of motion trajectories of point M as follows: For the non-trajectory return portion, as shown in Figure 9, the length of r3 changes to r 3_F1 →r 3_H1 ; Divided into two parts according to θ3>0 and θ3<0; When θ3=0, the length of BG1 / / AD,r is r 3_G1 ; For point G1, in △BDG1, according to the cosine theorem: Find the root and get r 3_G1 ; For point H1, when r4 and l BD When collinear, r3 has the shortest length r 3_H1 , then: r 3_H1 ＝l BD -r4(F10) When θ3>0, r 3_F1 →r 3_G1 Divide into n2 equal parts, take C 12 is any point, as shown in Figure 10; In △BC 12 In D, by the law of cosines, we get: In △ABD, r1, r2 and l BD As is known, θ5 is expressed as: From AD / / BG, we get: θ3=(θ8-θ5)>0(F13) Calculate the θ3 corresponding to each of the n2 equal parts, and get the motion trajectory of point M as follows: When θ3<0, r 3_G1 →r 3_H1 Divide into n3 equal parts, take C 13 is any point, as shown in Figure 11; Using the cosine theorem, we can get θ5 and θ8, then θ3=(θ8-θ5)<0. Calculate the θ3 corresponding to each of the n3 equal parts, and get the motion trajectory of point M as follows: The motion trajectory of the moving reference point M when there is a trajectory reversal is expressed as: When ∠BC1D≥90°, the solution is performed according to the solution method of the non-trajectory return part. When θ3>0, r 3_F1 →r 3_G2 Divide it into n4 equal parts, and the motion trajectory of point M is When θ3<0, r 3_G2 →r 3_H2 Divide into n5 equal parts, and get the motion trajectory of point M as follows: The motion trajectory of the moving reference point M is expressed as:

8. A method for solving the motion trajectory of a metamorphic four-bar mechanism according to claim 7, characterized in that: The ratio r2>r 21 and r4<r2<r 21 The specific method for solving the motion trajectory curve of the second stage of the variable cell four-bar mechanism motion in two cases is: When r2>r 21 When the length of r3 changes from r3→r 3_H2 ,Will Divide into n6 equal parts, take C 16 for any one of them; In △BC 16 In D, the law of cosines gives: In △ABD, the law of cosines gives: θ3 is calculated according to θ3=θ8-θ5; Calculate the θ3 corresponding to each of the n6 equal parts, and get the set of motion trajectories of point M as follows: When r4<r2<r 21 When r2<r4 is used, the solution is performed according to the solution method when r2<r4. First, it is determined whether there is a trajectory reversal. When it is determined that there is a trajectory reversal, the motion trajectory curve solution of the second stage of the metamorphic four-bar mechanism movement is divided into two parts: the trajectory reversal part and the non-trajectory reversal part for solution; when it is determined that there is no trajectory reversal, the motion trajectory curve solution of the second stage of the metamorphic four-bar mechanism movement is solved according to the non-trajectory reversal part; When it is determined that there is a trajectory return, the length of the trajectory return portion r3 changes to r3→r 3_E3 →r 3_F3 , r3→r 3_E3 Divide into n7 equal parts, and get the set of motion trajectories of point M as follows: The length of the untrajectory return portion r3 changes to r 3_F3 →r 3_H3 , r 3_F3 →r 3_H3 Divide into n8 equal parts, and get the set of motion trajectories of point M as follows: When there is a trajectory reversal, the motion trajectory set of point M is expressed as When it is determined that there is no trajectory reversal, the length of r3 changes to r3→r 3_H3 ; r3→r 3_H3 Divide into n9 equal parts, and get the set of motion trajectories of point M as follows:

9. A method for solving the motion trajectory of a metamorphic four-bar mechanism according to claim 8, characterized in that: When solving the motion trajectory curve of the third stage of the metamorphic four-bar mechanism motion in step S303, the solution is performed based on the symmetry between the motion trajectory of the third stage and the motion trajectory of the second stage about the straight line BD.

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