Kinematic analysis method for large translation lifting tongs type segmental assembling machine

Abstract

This invention relates to a kinematic analysis method for a large-translation lifting clamp-type segment assembly machine, comprising the following steps: analyzing the motion mechanism of the motion mechanism in the segment assembly machine, the motion mechanism including a lifting clamp, including double lifting cylinders and a non-isosceles V-shaped lifting beam with both ends hinged to the double lifting cylinders; the motion mechanism includes the lateral translation and rotation of the end of the assembly machine achieved by the differential telescoping of the double lifting cylinders in conjunction with the V-shaped lifting beam, the non-isosceles V-shaped lifting beam causing a lateral movement deviation at the end of the assembly machine; establishing a coordinate system based on the motion mechanism, wherein the differential telescoping motion of the double lifting cylinders in the lifting clamp is decomposed and a coordinate system is established for each; using a transformation matrix T to describe the pose transformation of the i-th coordinate system relative to the (i-1)-th coordinate system, a kinematic model of the assembly machine is established. This invention can achieve correct analysis of the end pose of the large-translation lifting clamp-type segment assembly machine, and the specific actions of the motion mechanism can be reverse-analyzed through the kinematic model.

Description

Technical Field

[0001] This invention relates to the field of shield tunneling technology, and in particular to a kinematic analysis method for a large-scale translational lifting clamp-type segment assembly machine. Background Technology

[0002] A tunnel boring machine (TBM) is a multi-system integrated underground engineering construction equipment that simultaneously excavates and constructs the tunnel structure. Due to its complex structure, the TBM's internal space is confined, with dim and uneven lighting and poor visibility. The assembly machine is a crucial component capable of six degrees of freedom of movement and positioning and installing complete ring segments. The weight of a single ring segment in a large-diameter TBM exceeds ten tons. Under heavy loads, the assembly machine is manually operated by segment assemblers using levers based on their accumulated experience, resulting in significant safety risks. With the increasing demands for efficiency in TBM construction, the need for rapid, unmanned assembly technology for TBM segments is urgent. One of the core issues is achieving analytical calculation of the assembly machine's end-effector posture, thereby determining the upstream target posture and coordinating the downstream assembly machine's joint motion control. Summary of the Invention

[0003] To address the aforementioned problems, this invention provides a kinematic analysis method for a large translational lifting clamp-type segment assembly machine, which can accurately analyze the end pose of the large translational lifting clamp-type segment assembly machine, and can also reverse analyze the specific movements of the motion mechanism through the kinematic model.

[0004] This invention is achieved through the following scheme: a kinematic analysis method for a large translational lifting clamp-type segment assembly machine, comprising the following steps:

[0005] Step S1: Analyze the motion mechanism of the motion mechanism in the segment assembly machine. The motion mechanism includes a lifting clamp, which includes a double lifting cylinder and a non-isosceles V-shaped lifting beam with both ends hinged to the double lifting cylinder. The motion mechanism includes the lateral translation and rotation of the end of the assembly machine by the differential telescoping of the double lifting cylinder in coordination with the V-shaped lifting beam. The non-isosceles V-shaped lifting beam causes a lateral movement deviation at the end of the assembly machine.

[0006] Step S2: Establish a coordinate system based on the motion mechanism, wherein the differential extension and retraction motion of the two lifting cylinders in the weightlifting clamp is decomposed into the same stroke motion of the two lifting cylinders and the single stroke motion of the single lifting cylinder, and coordinate systems are established based on the same stroke motion and the single stroke motion respectively.

[0007] Step S3: Describe the coordinate system O using the transformation matrix T. i X i Y i Z i Compared to O i-1 X i-1Y i-1 Z i-1 The pose transformation of i is an integer from 1 to n, and n is not less than 8. A kinematic model of the segment assembly machine is established.

[0008] A further improvement of the kinematic analysis method for the large translational lifting clamp-type segment assembly machine of the present invention is that the motion mechanism further includes a translational beam, a rotary table, a moving frame, double translational cylinders, a rotary motor, a deflection cylinder, a pitch cylinder, a small suction cup cylinder, and a segment suction cup. The double lifting cylinders are clamped and fixed on opposite sides of the rotary table. The V-shaped lifting beam is fastened to the outside of the rotary table. One end of the small suction cup cylinder is hinged to the intersection of the two beam arms of the V-shaped lifting beam. The other end of the small suction cup cylinder extends out of the V-shaped lifting beam and is hinged to a small suction cup located in the middle of the segment suction cup for suction of the capping block. The small suction cup is the end of the assembly machine.

[0009] The motion mechanism also includes: the dual translation cylinders pushing the moving frame to translate longitudinally along the translation beam; the rotary table rotating relative to the moving frame under the action of the rotary motor; the deflection cylinder driving the segment suction cup to achieve deflection motion; the pitch cylinder driving the segment suction cup to achieve pitch motion; and the small suction cup cylinder driving the small suction cup to achieve radial extension motion.

[0010] A further improvement of the kinematic analysis method for the large translational lifting clamp-type segment assembly machine of the present invention lies in that, during step S2:

[0011] Point O0 is the foot of the perpendicular line drawn from the center of the assembly machine's turntable to the vertical plane where the hinge points of the two translation cylinders and the translation beam are located. The opposite direction of the shield machine's advance direction is the positive direction of the Z0 axis, and the vertically upward direction is the positive direction of the Y0 axis. A right-hand rectangular coordinate system O0X0Y0Z0 is established.

[0012] Based on O0X0Y0Z0, the coordinate system O1X1Y1Z1 is obtained by shifting r1 in the Z0 direction and rotating γ1 around Z0, so that the backward extension of the Y1 axis points to the tube segment suction cup, and O1 is located on the vertical plane where the central axis of the double lifting cylinder is located.

[0013] Based on O1X1Y1Z1, move q2 along the Y1 axis to establish O2X2Y2Z2, so that O2 is located at the midpoint of the line connecting the moving ends of the double lifting cylinder in the fully retracted state;

[0014] Based on O2X2Y2Z2, move p3 and q3 along the X2 axis and Y2 axis respectively to establish O3X3Y3Z3, so that O3 is located at the intersection of the two beam arms of the V-shaped lifting beam when the double lifting cylinder moves in the same stroke.

[0015] Based on O3X3Y3Z3, move p4 and q4 along the X3 axis and Y3 axis respectively, and rotate γ4 around the Z3 axis to establish O4X4Y4Z4, so that O4 is located at the intersection of the two beam arms of the V-shaped lifting beam under the single stroke motion of a single lifting cylinder.

[0016] Based on O4X4Y4Z4, move p5 and q5 along the X4 axis and Y4 axis respectively to establish O5X5Y5Z5, so that O5 is located at the hinge point between the small suction cup and the small suction cup cylinder;

[0017] Based on O5X5Y5Z5, rotate β6 around the Y5 axis to establish O6X6Y6Z6, where β6 is the deflection angle of the tube segment suction cup caused by the stroke of the deflection cylinder.

[0018] Based on O6X6Y6Z6, rotate α7 around the X6 axis to establish O7X7Y7Z7, where α7 is the pitch angle of the segment suction cup caused by the stroke of the pitch cylinder;

[0019] Based on O7X7Y7Z7, move q8 along the Y7 axis to establish O8X8Y8Z8, where q8 is the radial extension displacement of the small suction cup caused by the stroke of the small suction cup cylinder.

[0020] A further improvement of the kinematic analysis method for the large translational lifting clamp-type segment assembly machine of the present invention lies in the fact that the transformation matrix... Where: R is the 3×3 attitude matrix at the end of the assembly machine; S is the 3×1 displacement matrix at the end of the assembly machine.

[0021] A further improvement of the kinematic analysis method for the large translational lifting clamp-type segment assembly machine of the present invention is that it also includes step S4: based on the kinematic model, considering the range of motion of the motion mechanism, performing inverse kinematic analysis.

[0022] This invention is based on fully considering the motion mechanism of the assembly machine's motion mechanism and establishing a more detailed coordinate system. In particular, for the motion mechanism with asymmetric motion, the coordinate system is established in the form of decomposed motion, so that the kinematic model can simulate the specific actions of the motion mechanism more precisely. This enables the correct analysis of the end pose of the large translational lifting clamp-type segment assembly machine. Correspondingly, the specific actions of the motion mechanism can be reverse-analyzed through the kinematic model, thereby enabling the large translational lifting clamp-type segment assembly machine to accurately achieve unmanned automated assembly. Attached Figure Description

[0023] Figure 1 This diagram illustrates the three-dimensional structure of a large-scale translational lifting clamp-type segment assembly machine. Figure 1 .

[0024] Figure 2This diagram illustrates the three-dimensional structure of a large-scale translational lifting clamp-type segment assembly machine. Figure 2 .

[0025] Figure 3 This diagram shows a partially enlarged structural schematic of a large-scale translational lifting clamp-type segment assembly machine.

[0026] Figure 4 A schematic diagram illustrating the construction process of each coordinate system in the method of the present invention is shown.

[0027] Figure 5 A schematic diagram of the equivalent triangle of the V-shaped lifting beam is shown.

[0028] Figure 6 This diagram illustrates the change in the equivalent triangle of the V-shaped lifting beam caused by the differential extension and retraction of the dual lifting cylinders. Figure 1 .

[0029] Figure 7 This diagram illustrates the change in the equivalent triangle of the V-shaped lifting beam caused by the differential extension and retraction of the dual lifting cylinders. Figure 2 .

[0030] Figure 8 A schematic diagram showing the correspondence between the stroke and deflection angle of the deflection cylinder in this invention is shown.

[0031] Figure 9 A schematic diagram showing the correspondence between the stroke of the pitch cylinder and the pitch angle in this invention is shown.

[0032] Figure 10 This invention illustrates a geometrical diagram of the reverse calculation of the differential telescopic motion of two lifting cylinders by considering the changes in the equivalent triangle of the known V-shaped lifting beam.

[0033] Figure 11 This diagram illustrates the parameter definitions of the motion mechanism in the segment assembly machine. Figure 1 .

[0034] Figure 12 This diagram illustrates the parameter definitions of the motion mechanism in the segment assembly machine. Figure 2 .

[0035] Figure 13 This diagram illustrates the parameter definitions of the motion mechanism in the segment assembly machine. Figure 3 .

[0036] Figure 14 This diagram illustrates the parameter definitions of the motion mechanism in the segment assembly machine. Figure 4 . Detailed Implementation

[0037] To address the issue that large-scale translational lifting clamp-type segment assembly machines cannot achieve unmanned automated assembly, this invention provides a kinematic analysis method for such machines. This method enables accurate analysis of the end-effector pose of the machine and allows for inverse kinematic analysis of the specific movements of the motion mechanism, thereby enabling precise unmanned automated assembly. The following detailed description, in conjunction with accompanying drawings, further illustrates this kinematic analysis method for large-scale translational lifting clamp-type segment assembly machines.

[0038] See Figures 1-3 As shown, a kinematic analysis method for a large-scale translational lifting clamp-type segment assembly machine includes the following steps:

[0039] Step S1: Analyze the motion mechanism of the segment assembly machine. This motion mechanism includes a lifting clamp 6, which comprises a double lifting cylinder 61 and a non-isosceles V-shaped lifting beam 62 hinged at both ends to the double lifting cylinder 61. The motion mechanism involves the differential telescoping of the double lifting cylinder 61 in conjunction with the V-shaped lifting beam 62 to achieve lateral translation and rotation at the end of the assembly machine. The non-isosceles V-shaped lifting beam 62 causes a lateral movement deviation at the end of the assembly machine.

[0040] Specifically, the motion mechanism also includes a translation beam 1, a rotary table 2, a moving frame 3, double translation cylinders 4, a rotary motor 5, a yaw cylinder 7, a pitch cylinder 8, a small suction cup cylinder 9, and a segment suction cup 10. Double lifting cylinders 61 are clamped and fixed to opposite sides of the rotary table 2, and the V-shaped lifting beam 62 is fastened to the outside of the rotary table 2. The V-shaped lifting beam 62 includes a fixed-length fixed beam arm 621 and a variable-length passive beam arm 622 (specifically as shown in the image). Figure 5 As shown, one end of the small suction cup cylinder 9 is hinged to the intersection of the two beam arms (i.e., the fixed beam arm 621 and the passive beam arm 622) of the V-shaped lifting beam 62. The other end of the small suction cup cylinder 9 extends out of the V-shaped lifting beam 62 and is hinged to the small suction cup 101 located in the middle of the segment suction cup 10 for suction of the capping block. The small suction cup 101 is the end of the assembly machine. Specifically, the segment suction cup 10 is composed of three suction cup units. The middle suction cup unit is the small suction cup 101, which is hinged to the other two suction cup units on both sides. When the three suction cup units are on the same surface, the segment suction cup 10 is formed for suctioning large segments. The deflection cylinder 7 and the pitch cylinder 8 act on the two suction cup units on the sides, while the small suction cup cylinder 9 only acts on the small suction cup 101.

[0041] The motion mechanism also includes: the double translation cylinder 4 pushes the moving frame 3 to move longitudinally along the translation beam 1; the turntable 2 rotates relative to the moving frame 3 under the action of the rotary motor 5 (i.e., large rotational motion); the deflection cylinder 7 drives the segment suction cup 10 to achieve deflection motion; the pitch cylinder 8 drives the segment suction cup 10 to achieve pitching motion; the small suction cup cylinder 9 drives the small suction cup 101 (i.e., the end of the assembly machine) to achieve radial extension motion, so as to suck the segment capping block.

[0042] Step S2: Establish a coordinate system based on the motion mechanism. Specifically, the differential extension and retraction motion of the double lifting cylinders 61 in the weightlifting clamp 6 is decomposed into the same stroke motion of the double lifting cylinders 61 and the single stroke motion of the single lifting cylinder, and coordinate systems are established based on the same stroke motion and the single stroke motion, respectively.

[0043] Specifically: In the coordinate transformation from the (i-1)th to the ith coordinate, let counterclockwise rotation be positive, the direction along the axis be positive, and the angle of rotation around the X-axis be denoted as α. i The angle of rotation about the Y-axis is denoted as β. i The angle of rotation about the Z-axis is denoted as γ. i The amount of translation along the X-axis is denoted as p. i The amount of translation along the Y-axis is denoted as q. i The amount of translation along the Z-axis is denoted as r. i When calculating the end-effector posture of the assembly machine, the rotation is first around the Z-axis, then around the Y-axis (i.e., the Y-axis transformed from the Z-axis), and finally around the X-axis (same as above).

[0044] After making the above settings, begin establishing the coordinate system, in conjunction with... Figure 4 As shown:

[0045] (1) Draw a perpendicular line from the center of the rotary table 2 of the assembly machine to the vertical plane where the hinge points of the two translation cylinders 4 and the translation beam 1 are located. The foot of the perpendicular is point O0. The opposite direction of the tunnel boring machine's advance is the positive direction of the Z0 axis, and the vertically upward direction is the positive direction of the Y0 axis. Establish a right-hand rectangular coordinate system O0X0Y0Z0. Use this world coordinate system O0X0Y0Z0 as the basic coordinate system.

[0046] (2) Based on O0X0Y0Z0, shift r1 in the Z0 direction (i.e., the translation amount along the translation beam 1) and rotate γ1 around Z0 (i.e., the large rotation angle) to obtain the coordinate system O1X1Y1Z1, so that the reverse extension line of the Y1 axis points to the tube segment suction cup 10, and O1 is located on the vertical plane where the central axis of the double lifting cylinder 61 is located.

[0047] (3) Based on O1X1Y1Z1, move q2 along the Y1 axis to establish O2X2Y2Z2, so that O2 is located at the midpoint of the line connecting the moving ends of the double lifting cylinder 61 in its fully retracted state.

[0048] (4) Based on O2X2Y2Z2, move p3 and q3 along the X2 and Y2 axes respectively to establish O3X3Y3Z3, so that O3 is located at the intersection of the two beam arms of the V-shaped lifting beam 62 under the same stroke movement of the double lifting cylinder 61. Wherein, p3 is the displacement of the coordinate system in the X direction caused by the non-isosceles triangle constructed by the V-shaped lifting beam 62 under the same stroke of the double lifting cylinder 61; q3 is the smaller value of the stroke in the double lifting cylinder 61.

[0049] (5) Based on O3X3Y3Z3, move p4 and q4 along the X3 axis and Y3 axis respectively and rotate γ4 around the Z3 axis (i.e., the small rotation angle of the segment suction cup 10) to establish O4X4Y4Z4, so that O4 is located at the intersection of the two beam arms of the V-shaped lifting beam 62 under the single stroke motion of the single lifting cylinder.

[0050] (6) Based on O4X4Y4Z4, move p5 and q5 along the X4 axis and Y4 axis respectively to establish O5X5Y5Z5, so that O5 is located at the hinge point between the small suction cup 101 and the small suction cup cylinder 9.

[0051] (7) Based on O5X5Y5Z5, rotate β6 around the Y5 axis to establish O6X6Y6Z6, where β6 is the deflection angle of the tube segment suction cup 10 caused by the stroke of the deflection cylinder.

[0052] (8) Based on O6X6Y6Z6, rotate α7 around the X6 axis to establish O7X7Y7Z7, where α7 is the pitch angle of the tube segment suction cup 10 caused by the stroke of the pitch cylinder.

[0053] (9) Move q8 along the Y7 axis on the basis of O7X7Y7Z7 to establish O8X8Y8Z8, where q8 is the radial extension displacement of the small suction cup 101 caused by the stroke of the small suction cup cylinder.

[0054] The above-described coordinate system establishment method is only a preferred embodiment. Steps (4) and (5) establish coordinate systems based on the motion decomposition of the asymmetric lifting clamp 6. By establishing coordinate systems through decomposition, the kinematic model can more accurately represent the motion of the asymmetric motion mechanism, thereby enabling more accurate attitude analysis. Of course, in actual coordinate system establishment, coordinate systems can be established for other asymmetric motion mechanisms in the segment assembly machine based on the idea of ​​coordinate system establishment in this embodiment. In principle, the more coordinate systems there are, the more accurate the model will be.

[0055] Step S3: Describe the coordinate system O using the transformation matrix T. i X i Y i Z i Compared to O i-1 Xi-1 Y i-1 Z i-1 The pose transformation of i is an integer from 1 to n, and n is not less than 8. A kinematic model of the segment assembly machine is established.

[0056] Specifically: Suppose that there exists a certain vector in the coordinate system {A}. and The coordinate components in another coordinate system {B} are Then there exists a transformation matrix T such that When the {B} coordinate system is rotated from the A coordinate system around the X, Y, and Z axes When the angles θ and ψ are obtained, then,

[0057]

[0058] However, this calculation method cannot take into account coordinate system translation transformations. Therefore, this implementation proposes an improved transformation matrix:

[0059] Rotate about the X-axis by an angle α:

[0060]

[0061] Rotate about the Y-axis by an angle β:

[0062]

[0063] Rotation angle γ around the Z-axis:

[0064]

[0065] Translate a, b, and c along the X, Y, and Z axes respectively:

[0066]

[0067] final, Where R is a 3×3 matrix, representing the components of a set of basis vectors of orthogonality of the segment with a magnitude of 1 in the world coordinate system, and P is a 3×1 matrix (vector), representing the position of the segment in the world coordinate system.

[0068] The calculation process for the correct solution is explained further below:

[0069] The geometric solution method for the pose change of the differential extension (i.e., stroke difference) stroke of a dual-lift hydraulic cylinder is as follows:

[0070] 1.1 First, cooperate Figure 5 As shown, the V-shaped lifting beam 62 can be equivalent to triangle ABC, where AB is the fixed beam arm 621, BC is the passive beam arm 622, and BD is the perpendicular line drawn from the intersection of the two beam arms to the line connecting AC.

[0071] 1.2 When the stroke of the lifting cylinder hinged to the passive beam arm 622 is greater than the stroke of the lifting cylinder hinged to the fixed beam arm 621, such as Figure 6 As shown.

[0072] The solution steps are as follows: Given: BD⊥AC; the side lengths and angles of the original triangle ABC; A′B′, ∠A′B′C′, and CC′ in the new triangle A′B′C′. Find: BB′, ∠B′BD, ∠BAB′ (i.e., γ4).

[0073] Find the length of A′C′ using the Pythagorean theorem:

[0074]

[0075] Find ∠CAC using trigonometric functions:

[0076]

[0077] Solve triangle A′B′C′:

[0078]

[0079] ∠C′A′B′=180°-∠A′B′C′-∠A′C′B′

[0080] Find ∠BAB′ and ∠CAB′:

[0081] γ4=∠BAB′=∠C′A′B′+∠CAC′-∠CAB

[0082] ∠CAB′=∠C′A′B′+∠CAC′

[0083] Find BB' in triangle BAB':

[0084]

[0085] Find ∠B′BD:

[0086] In triangle B′AD,

[0087]

[0088] In triangle BDB′,

[0089]

[0090] final,

[0091] q4=BB′×cos(180°-∠B′BD)

[0092] p4=BB′×sin(180°-∠B′BD)

[0093] Note: Angle γ4 is a positive value, displacement in the Y direction is a negative value, and displacement in the X direction is a positive value.

[0094] 1.3 When the stroke of the lifting cylinder hinged to the passive beam arm 622 is less than the stroke of the lifting cylinder hinged to the fixed beam arm 621, such as Figure 7 As shown.

[0095] The solution steps are as follows: Given: BD⊥AC; the side lengths and angles of the original triangle ABC; A′B′, ∠A′B′C′, and AA′ in the new triangle A′B′C′. Find: BB′, ∠B′BD, ∠BCB′ (i.e., γ4).

[0096] Find the length of A′C′ using the Pythagorean theorem:

[0097]

[0098] Find ∠ACA′ using trigonometric functions:

[0099]

[0100] Solve triangle A′B′C′:

[0101]

[0102] ∠C′A′B′=180°-∠A′C′B′-∠A′B′C′

[0103]

[0104] Find ∠BCB′ and ∠ACB′:

[0105] γ4=∠BCB′=∠A′C′B′+∠ACA′-∠ACB

[0106] ∠ACB′=∠ACB+∠BCB′

[0107] Find BB' in triangle BCB':

[0108]

[0109] Find ∠B′BD:

[0110] In triangle B′CD,

[0111]

[0112] In triangle BDB′,

[0113]

[0114] final,

[0115] q4=BB′×cos(180°-∠B′BD)

[0116] p4=BB′×sin(180°-∠B′BD)

[0117] Note: Angle γ4 is negative, the displacement in the Y direction is negative, and the displacement in the X direction is also negative.

[0118] 1.4 The geometric calculation method for the deflection angle caused by the deflection cylinder is as follows, in conjunction with... Figure 8 As shown:

[0119] β6=Atan2(δ 偏转 ,d1)

[0120] Among them: the extension of the deflection cylinder 7 causes the segment suction cup 10 to deflect counterclockwise, so the sign of β6 is consistent with δ.

[0121] 1.5 The geometric calculation method for the pitch angle caused by the stroke of the pitch cylinder is as follows, in conjunction with... Figure 9 As shown:

[0122] α7=Atan2(δ 俯仰 ,d2)

[0123] Among them: the extension of the pitch cylinder 8 causes the segment suction cup 10 to deflect counterclockwise, so the sign of α7 is consistent with δ.

[0124] 1.6. Based on the coordinate systems and transformation matrices in the kinematic model, calculate the transformation matrices between the coordinate systems in this embodiment. i = 1 to 8:

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

[0132]

[0133] Then the total transformation matrix R is the 3×3 attitude matrix at the end of the assembly machine; S is the 3×1 displacement matrix at the end of the assembly machine.

[0134] 1.7、calculation:

[0135]

[0136] Among them:

[0137] r 11 =cosβ6(cosγ1cosγ4-sinγ1sinγ4)

[0138] r 12 =cosα7(-cosγ4sinγ1-cosγ1sinγ4)+sinα7sinβ6(cosγ1cosγ4-sinγ1sinγ4)

[0139] r 13 =-sinα7(-cosγ4sinγ1-cosγ1sinγ4)+cosα7sinβ6(cosγ1cosγ4-sinγ1sinγ4)

[0140] r 21 =cosβ6(cosγ4sinγ1+cosγ1sinγ4)

[0141] r 22 =sinα7sinβ6(cosγ4sinγ1+cosγ1sinγ4)+cosα7(cosγ1cosγ4-sinγ1sinγ4)

[0142] r 23 =cosα7sinβ6(cosγ4sinγ1+cosγ1sinγ4)-sinα7(cosγ1cosγ4-sinγ1sinγ4)

[0143] r 31 =-sinβ6

[0144] r 32 =cosβ6sinα7

[0145] r 33 =cosα7cosβ6

[0146] s1=-q2sing1+p3cosγ1-q3sing1+p4cosγ1-q4sing1+p5(cosγ1cosγ4-sing1sing4)-q5(sing1cosγ4+cosγ1sing4)+q8·r 12

[0147] s2=q2cosγ1+p3sing1+q3cosγ1+p4sing1+q4cosγ1+p5(sing1cosγ4+cosγ1sing4)+q5(cosγ1cosγ4-sing1sing4)+q8·r 22

[0148] s3=r1+q8cosβ6sinα7

[0149] get more info:

[0150] r 11 =cosβ6cos(γ1+γ4) (1.1)

[0151] r 12 =-cosα7sin(γ1+γ4)+sinα7sinβ6cos(γ1+γ4) (1.2)

[0152] r 13 =sinα7sin(γ1+γ4)+cosα7sinβ6cos(γ1+γ4) (1.3)

[0153] r 21 =cosβ6sin(γ1+γ4) (1.4)

[0154] r 22 =sinα7sinβ6sin(γ1+γ4)+cosα7cos(γ1+γ4) (1.5)

[0155] r 23 =cosα7sinβ6sin(γ1+γ4)-sinα7cos(γ1+γ4) (1.6)

[0156] r 31 =-sinβ6 (1.7)

[0157] r 32 =cosβ6sinα7 (1.8)

[0158] r 33 =cosα7cosβ6 (1.9)

[0159] s1=-q2sinγ1+p3cosγ1-q3sinγ1+p4cosγ1-q4sinγ1+p5cos(γ1+γ4)-q5sin(γ1+γ4)+q8·r 12 (1.10)

[0160] s2=q2cosγ1+p3sinγ1+q3cosγ1+p4sinγ1+q4cosγ1+p5sin(γ1+γ4)+q5cos(γ1+γ4)+q8·r 22 (1.11)

[0161] s3=r1+q8cosβ6sinα7 (1.12)

[0162] Empirical calculations show that the attitude matrix components... Orthogonal, and ||R i ||=1.

[0163] The inverse kinematics yields the following attitudes (ZYX guide): small slewing angle γ4, yaw angle β5, and pitch angle α6 at the end of the assembly machine.

[0164]

[0165] β6=arcsin(-r 31 )

[0166]

[0167] As a preferred embodiment, this method can also establish the inverse kinematic equation of the segment assembly machine based on the above-mentioned kinematic model, taking into account the range of motion of the motion mechanism.

[0168] In summary, based on the end-effector attitude matrix and displacement matrix (vector) of the assembly machine obtained from the forward kinematics, the rotation and displacement of the assembly machine's motion mechanism (including each movable joint) can be solved. Furthermore, by combining structural design parameters, the extension / retraction of each cylinder and the maximum rotation angle of the assembly machine can be obtained. Specifically, the known quantities are: the positions of the segment suction cups s1, s2, and s3, the total rotation angle γ of the segment suction cups, the deflection angle β5 of the segment suction cups, and the pitch angle α6 of the segment suction cups. The target quantities to be solved are: the maximum translation r1, the maximum rotation angle γ1, the same stroke amount q3 of the two lifting cylinders, the stroke difference δ of the two lifting cylinders, and the stroke amount c of the deflection cylinder. 偏转 And the stroke of the pitch cylinder c 俯仰 .

[0169] The following is a further explanation of the analytical calculation process for the inverse solution:

[0170] 2.1 Given: The attitude matrix of the assembly machine end effector is associated with the following variables as shown in formulas (1.1) to (1.12) above.

[0171] The independence of γ1 and γ4 indicates that:

[0172] γ1=γ-γ4 (1.13)

[0173] The aforementioned p4, q4, and δ can be obtained from structural parameters, that is:

[0174] {p4, q4, δ}=f(γ4) (1.14)

[0175] {p4, q4, δ}=f(γ1) (1.15)

[0176] Combining formulas (1.10), (1.11), and (1.12), we obtain the following formula:

[0177]

[0178] The equations are: γ1, q3, and r1 are unknown; the first two equations are a system of two transcendental equations in γ1 and q3, which can be obtained using Newton's iteration method; r1 is an independent variable, which can be obtained from the third equation.

[0179] r1=s3-q8cosβ6sinα7 (2.17)

[0180] 2.2 Cooperation Figure 10 As shown, given: BD⊥AC; the side lengths and angles of the original triangle ABC; in the new triangle A′B′C′, A′B′ and ∠A′B′C′; ∠ACB′=ψ. Find: ∠B′BD, AA′.

[0181] At this point, if h is found to be positive, the stroke of the lifting cylinder hinged to the passive beam arm 622 is greater than the stroke of the lifting cylinder hinged to the fixed beam arm 621; if h is found to be negative, the stroke of the lifting cylinder hinged to the fixed beam arm 621 is greater than the stroke of the lifting cylinder hinged to the passive beam arm 622.

[0182] Specifically, such as Figure 10 As shown, x0, x1 > 0; y0, y1 < 0, y1 = -tanψ·x1.

[0183]

[0184]

[0185] but,

[0186]

[0187] again,

[0188]

[0189] Combining formulas (2.1) and (2.2), we get...

[0190]

[0191] Substitute,

[0192]

[0193] Combining formulas (2.2) and (2.3), and eliminating x1, we get...

[0194]

[0195] This is a quadratic equation in one variable h, which simplifies to...

[0196]

[0197]

[0198] Then we can solve for h.

[0199]

[0200] Since h < 0 and h is a relatively small value, ± is taken as +.

[0201] Substituting formula (2.4) back into formula (2.3),

[0202]

[0203] In formula (2.5), the denominator of the fraction

[0204]

[0205] The numerator of the fraction in formula (2.5)

[0206]

[0207] Then formula (2.5)

[0208]

[0209] but

[0210]

[0211] In this case, p4, q4, and γ4 are all negative.

[0212]

[0213]

[0214] γ4=-∠BCB′

[0215] Iterative equations

[0216] f1=(p3+x1-x0)cosγ1-(q2+q3)sinγ1-(y1-y0)sinγ1+p5cosγ-q5sinγ+q8·r 12 -s1

[0217] f2=(p3+x1-x0)sinγ1+(q2+q3)cosγ1+(y1-y o cosγ1+p5sinγ+q5cosγ+q8·r 22 -s2

[0218] Calculate partial derivatives

[0219] ψ=∠ACB-γ4=∠ACB+γ1-γ

[0220]

[0221] but,

[0222]

[0223]

[0224] but,

[0225]

[0226]

[0227]

[0228]

[0229] Newton iterations can be performed on γ1 and q3, with the following iteration form:

[0230]

[0231] 2.3, See reference Figure 8 As shown, the inverse kinematics solution formula for the deflection cylinder is as follows:

[0232] c 偏转 =d1·tanβ6

[0233] c 偏转 The symbol is the same as β6.

[0234] 2.4, See reference Figure 9 As shown, the inverse kinematics solution formula for the pitch cylinder is:

[0235] c 俯仰 =d2·tana7

[0236] c俯仰 The symbol is the same as α7.

[0237] This invention performs cross-calibration between the algorithm's internal testing and the 3D model. The specific steps are as follows:

[0238] 3.1 Structural parameter definitions of key motion mechanisms of the assembly machine, please refer to... Figures 11-14 As shown.

[0239] When the L1-double translation cylinder is at zero stroke position, the horizontal distance from the hinge point of its base to the vertical plane containing the central axis of the double lifting cylinder.

[0240] When the L2-double lifting cylinder is at zero stroke, the vertical distance from the center of the hinge point of its movable end to the horizontal plane where the center of the rotary table is located.

[0241] The horizontal distance between the centers of the hinge points of the moving ends of the L3 double lifting cylinder when the stroke is at zero position.

[0242] When the L4' and L4- double lifting cylinders are at zero stroke position, the distance between the center of the hinge point of the moving end of the double lifting cylinder and the intersection point of two lines that pass through the center of the hinge point of the double lifting cylinder and are parallel to the two beam arms of the V-shaped lifting beam.

[0243] L5 - The distance between the center of the hinge point of the double lifting cylinder and the intersection of two lines parallel to the two arms of the V-shaped lifting beam, and the center of the hinge point of the movable end of the small suction cup cylinder.

[0244] The distance between the center of the hinge point of the L6 pitch cylinder's moving end and the center of pitch rotation.

[0245] The distance between the center of the hinge point on the moving end of the L7 deflection cylinder and the deflection center.

[0246] 3.2 Internal Testing of Kinematic Algorithm. First, fix the parameters (length: mm; angle: °): L1 = 1445, L2 = 3180, L3 = 6390, L4 = 3359.37, L4' = 3359.47, L5 = 148.88, L6 = 500, L7 = 500, small suction cup cylinder extension = 0, horizontal offset p5 = 0 from the intersection of the axes of the two beam arms of the V-shaped lifting beam to the axis of the small suction cup cylinder, initial extension of the yaw cylinder = 25, initial extension of the pitch cylinder = 30. Then, perform forward and inverse kinematic analysis using the kinematic model, and compare the analytical results, as detailed in Tables 1, 2, and 3.

[0247] Table 1. Input parameters for the correct solution (Length: mm; Angle: °)

[0248]

[0249]

[0250] Table 2. Inverse kinematics input parameters (length: mm; angle: °)

[0251]

[0252]

[0253] Table 3. Cross-calibration between kinematic algorithm and 3D model

[0254]

[0255]

[0256] The comparison results above show that the analytical results of forward and inverse kinematics using the kinematic model of this invention are very close to the actual measurement results, indicating high model accuracy.

[0257] The present invention has been described in detail above with reference to the accompanying drawings and embodiments. Those skilled in the art can make various modifications to the present invention based on the above description. Therefore, certain details in the embodiments should not be construed as limiting the present invention, and the scope of protection of the present invention shall be defined by the appended claims.

Claims

1. A kinematic analysis method for a large-scale translational lifting clamp-type segment assembly machine, characterized in that, Including the following steps: Step S1: Analyze the motion mechanism of the motion mechanism in the segment assembly machine. The motion mechanism includes a lifting clamp, which includes a double lifting cylinder and a non-isosceles V-shaped lifting beam with both ends hinged to the double lifting cylinder. The motion mechanism includes the lateral translation and rotation of the end of the assembly machine by the differential telescoping of the double lifting cylinder in coordination with the V-shaped lifting beam. The non-isosceles V-shaped lifting beam causes a lateral movement deviation at the end of the assembly machine. Step S2: Establish a coordinate system based on the motion mechanism. The differential extension and retraction motion of the double lifting cylinders in the weightlifting clamp is decomposed into the same stroke motion of the double lifting cylinders and the single stroke motion of the single lifting cylinder. Based on the same stroke motion and the single stroke motion, establish an same stroke coordinate system and a single stroke coordinate system respectively. The origin of the same stroke coordinate system is located at the intersection of the two beam arms of the V-shaped lifting beam under the same stroke motion of the double lifting cylinders. The origin of the single stroke coordinate system is located at the intersection of the two beam arms of the V-shaped lifting beam under the single stroke motion of the single lifting cylinder. The single stroke coordinate system can be obtained by transforming the same stroke coordinate system by moving a specified distance along the X-axis and Y-axis and rotating a specified angle around the Z-axis. Step S3: Describe the coordinate system using the transformation matrix T. Compared to pose transformation, Let n be an integer from 1 to n, where n is not less than 8. Establish a kinematic model of the segment assembly machine.

2. The kinematic analysis method for the large translational lifting clamp-type segment assembly machine as described in claim 1, characterized in that, The motion mechanism also includes a translation beam, a turntable, a moving frame, double translation cylinders, a rotary motor, a deflection cylinder, a pitch cylinder, a small suction cup cylinder, and a segment suction cup. The double lifting cylinders are clamped and fixed on opposite sides of the turntable. The V-shaped lifting beam is fastened to the outside of the turntable. One end of the small suction cup cylinder is hinged to the intersection of the two beam arms of the V-shaped lifting beam. The other end of the small suction cup cylinder extends out of the V-shaped lifting beam and is hinged to the small suction cup located in the middle of the segment suction cup for suction of the top sealing block. The small suction cup is the end of the assembly machine. The motion mechanism also includes: the dual translation cylinders pushing the moving frame to translate longitudinally along the translation beam; the rotary table rotating relative to the moving frame under the action of the rotary motor; the deflection cylinder driving the segment suction cup to achieve deflection motion; the pitch cylinder driving the segment suction cup to achieve pitch motion; and the small suction cup cylinder driving the small suction cup to achieve radial extension motion.

3. The kinematic analysis method for the large translational lifting clamp-type segment assembly machine as described in claim 2, characterized in that, When performing step S2: The foot of the perpendicular line drawn from the center of the assembly machine's rotary table to the vertical plane containing the hinge points of the two translation cylinders and the translation beam is... The point is the opposite direction of the tunnel boring machine's advance direction. The positive direction of the axis, the vertically upward direction is Establish a right-handed rectangular coordinate system along the positive axis. ; exist On the basis of Directional displacement and around Rotation Obtain the coordinate system ,make The reverse extension of the axis points towards the segment suction cup, so that... Located on the vertical plane where the central axis of the double lifting cylinder is located, For the large turning angle of the assembly machine; exist Based on Axial movement ,Establish ,make Located at the midpoint of the line connecting the moving ends of the double lifting cylinders in their fully retracted state; exist Based on each along Axial movement Establish the same travel coordinate system This positions O3 at the intersection of the two arms of the V-shaped lifting beam when the two lifting cylinders move in the same stroke. exist Based on each along Axial movement And around Axis rotation Establish a single travel coordinate system This positions O4 at the intersection of the two arms of the V-shaped lifting beam during a single stroke of the single lifting cylinder. For the small rotation angle of the segment suction cup; exist Based on each along Axial movement ,Establish This positions O5 at the hinge point between the small suction cup and the small suction cup cylinder. exist Based on Axis rotation ,Establish , The deflection angle of the segment suction cup caused by the stroke of the deflection cylinder; exist Based on Axis rotation ,Establish , The pitch angle of the segment suction cup caused by the stroke of the pitch cylinder; exist Based on Axis movement ,Establish , The radial extension displacement of the small suction cup caused by the stroke of the small suction cup cylinder.

4. The kinematic analysis method for the large translational lifting clamp-type segment assembly machine as described in claim 1, characterized in that, The transformation matrix Where: R is the 3×3 attitude matrix of the end of the assembly machine; S is the 3×1 displacement matrix of the end of the assembly machine.

5. The kinematic analysis method for the large translational lifting clamp-type segment assembly machine as described in claim 1, characterized in that, It also includes step S4: based on the kinematic model, considering the range of motion of the motion mechanism, perform inverse kinematic analysis.

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