CN105619449B - A kind of zero drift spring gravity compensation method based on force feedback equipment - Google Patents
A kind of zero drift spring gravity compensation method based on force feedback equipment Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J18/00—Arms
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/10—Programme-controlled manipulators characterised by positioning means for manipulator elements
- B25J9/109—Programme-controlled manipulators characterised by positioning means for manipulator elements comprising mechanical programming means, e.g. cams
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Abstract
A kind of zero drift spring gravity compensation method based on force feedback equipment, (1) the gravity compensation spring one end of large arm is connected to the spring on pedestal deceleration mechanism driven wheel and is fixedly mounted face, the other end by steel wire rope be connected by fixed pulley be connected on large arm deceleration mechanism driven wheel at large arm reverse extending line and driven wheel edge interface point；(2) the gravity compensation spring one end of forearm is connected to the spring on pedestal deceleration mechanism driven wheel and face is fixedly mounted, the other end is connected by steel wire rope to be connected to by fixed pulley at forearm deceleration mechanism driven wheel edge interface point.Present invention alleviates the inertia of the big arm mechanism of force feedback equipment either small arm mechanism, avoid steel wire rope and are interfered on certain positions with big arm mechanism or small arm mechanism.And fully consider the influence of the radius length and installation site of fixed pulley to gravity compensation, it was demonstrated that the spring gravity compensation method can realize complete gravity compensation to force feedback equipment.
Description
Technical Field
The invention relates to a zero free length spring gravity compensation method of force feedback equipment.
Background
Force feedback equipment often uses spring compensation gravity, and its advantage lies in: the spring is lightweight and does not add excessive weight and inertia to the force feedback device, thereby affecting the operational performance of the force feedback device. In the force feedback device, there are various methods for gravity compensation using a spring: simple spring gravity compensation, zero free length spring gravity compensation and cam spring gravity compensation, and some other spring gravity compensation means.
By simple spring gravity compensation is meant without the aid of other auxiliary equipment, such as: small wheels, connecting rods, irregular cams, etc., which use only springs for gravity compensation of the force feedback device. In the method, one end of a spring is connected to an operating arm of the force feedback device to be compensated, and the other end of the spring is fixed on a fixed bracket of the force feedback device. In general engineering applications, in order to reduce the complexity of spring design, a linear spring is often used to replace a nonlinear spring, and the stiffness coefficient of the linear spring is usually obtained by taking the average value of the gravity compensation amount required when the connecting rod required to compensate gravity is at different angles to find the average stiffness coefficient of the spring, and using the average stiffness coefficient as the stiffness coefficient of the linear spring, thereby realizing the gravity compensation of the connecting rod. However, since the spring is directly connected to the force feedback device operating arm to be compensated, mechanical interference between the spring and the link in a part of the movement space is easily caused. In order to avoid the influence of the existence, the AhmadMashayekhi skillfully installs the spring on the driven wheel of the speed reducing mechanism instead of directly connecting with the operating arm of the force feedback device, and designs a simple spring gravity compensation mode with novel structure (see: VirSense: a novel gravity device with fixed-base motors and a gravity compensation system, Industrial robot: An International Journal,2014,41(1): 37-49.). However, the Ahmad Mashayekhi design method only artificially gives the position of the spring connecting point, and when the spring gravity compensation is designed, an optimal spring gravity compensation mathematical model is not established, and the optimal spring connecting point position, the optimal free length and the optimal average stiffness coefficient of the spring for gravity compensation are not considered. Aiming at the problems, Lichunquan and the like provide an optimal spring gravity compensation method for force feedback equipment based on an improved simple particle algorithm, a spring is arranged on a linear transmission speed reduction driven wheel of a large arm and a small arm of the force feedback equipment, the influence of the connecting point position, the free length and the stiffness coefficient of the spring on gravity compensation is fully considered, a gravity compensation model with a nonlinear constraint relation is established, a stretching free length ratio is introduced, the connecting point position and the stretching free length ratio are used as optimization quantities, an average moment error is used as an optimized fitness function, and iterative optimization is carried out by using the improved simple particle optimization algorithm, so that an arm mechanism of the force feedback equipment can obtain the optimal spring gravity compensation.
In simple spring gravity compensation, although the above method can perform gravity compensation, complete spring gravity compensation of the force feedback device cannot be realized because the free length of the spring is not zero, and if complete gravity compensation is required, the designed spring stiffness coefficient is necessarily non-linear. However, in actual engineering, a linear spring is used instead of the actual non-linear spring rate. Therefore, a force feedback device cannot be fully gravity compensated with a simple linear spring. In order to realize the sufficient compensation of the force feedback Device by Using a linear Spring, the Rongfang Fan uses the linear Spring, a fixed pulley and a steel wire rope, the fixed pulley is arranged on a PHANToM premium1.5 operating arm, one end of the steel wire rope is fixed on the operating arm and is connected on a fixed bracket of the force feedback Device after being tangent with the fixed pulley, a gravity compensation mode of a Spring with zero free length is designed (see the details: Improvement of Dynamic transmission of a capacitive Device by Using Spring Balance C, Proceedings of the 2012IEEE International Conference on Robotics and B principles, 2012: 1075-1080.), and when the radius of the fixed pulley and the length of a fixed shaft of the fixed pulley are both equal to zero, the method can obtain the complete gravity compensation. In practical designs, it is always difficult to ensure that the radius of the pulley and the fixed position length of the pulley are both zero at the same time, and in addition, the connection between the pulley and the wire rope is always subject to friction, which results in a compensation deviation also in the fully gravity-compensated version of a zero free length spring. Compared with simple spring gravity compensation, the zero free length spring gravity compensation mode needs to additionally increase a steel wire rope and a fixed pulley, and the fixation and installation are complex relative to the former. In addition, as with simple spring gravity compensation, the pulleys and the wire rope can interfere with the mechanism of the force feedback operating arm at certain positions, and the working space of the connecting rod is affected. Furthermore, in the method of Rongfang Fan, gravity compensation is performed only on a single manipulator arm in PHANToM premium1.5. In fact, in the zero free length spring gravity compensation method in the method proposed by Rongfang Fan, the fixed pulley and the steel wire rope are respectively installed on the big arm and the small arm which are connected end to end of the force feedback device, and the gravity compensation of the method for the small arm is invalid at the moment because the relative positions of the big arm and the small arm are continuously changed in the operation process. Furthermore, the link, pulley and cable on the small arm and the large arm move relative to each other, which may cause the spring and cable on the large arm to interfere with each other at some positions, or may have some positions, so that the spring on the large arm is completely loose and cannot achieve the compensation effect. Therefore, such zero free length spring gravity compensation methods employing linear springs, fixed pulleys and wire ropes mounted on the operating arm of a series force feedback device are also deficient.
The gravity compensation mode of the cam spring can also realize the gravity compensation of the force feedback equipment. The Omega force feedback device uses a spring, a wire rope and a cam formed by combining a single irregular circumference to perform gravity compensation on the force feedback device (patent number: US 8,188,843B 2). Rongfang Fan also uses a gravity compensation method similar in principle to the combination of the Omega force feedback Device cam Spring for gravity compensation in PHONTOM premium1.5 (see in detail: improvement of Dynamic transfer of Haptical Device by Using Spring Balance [ C ]. Proceedings of the 2012IEEE International Conference on Robotics and Biometrics, 2012: 1075-1080.). The cam spring gravity compensation mode can also completely compensate the gravity of the operating arm of the force feedback device, which is the biggest advantage of the mode. However, this compensation method also has the following problems: firstly, the cam needs to be additionally designed and processed when gravity compensation is carried out, and the cam needs to be installed on a transmission shaft of a connecting rod of the existing force feedback equipment, so that the cost and the complexity of design and installation are increased; secondly, because the radius of the cam is a function taking the rotation angle of the cam as an independent variable, when the force feedback equipment moves rapidly, a steel wire rope connecting the cam and the spring cannot be always kept on the same plane, so that a stretching gap is generated between the spring and the steel wire rope, a time delay amount is introduced, the time delay amount is similar to a tooth side gap between gears, the spring and the steel wire rope are easy to slide, and the stability of the force feedback system is also reduced.
The above mentioned spring gravity compensation method is mainly used for gravity compensation in the force feedback device. In addition, there are many other spring gravity compensation methods, which are not used in force feedback devices in the prior art documents and patents. Although those spring gravity compensation methods have advantages, they are either complex in design and not easily implemented and retrofitted onto existing force feedback devices, or designed for some specific mechanism and not of general significance in the design of gravity compensation for force feedback devices.
In summary, by analyzing the characteristics of the spring gravity compensation methods of various force feedback devices, we disclose a zero free length spring gravity compensation method based on force feedback devices, wherein a spring and a fixed pulley for gravity compensation of the force feedback devices are respectively installed on a spring fixing installation surface on a driven wheel of a base mechanism of the force feedback devices, one end of the spring is connected with one end of a steel wire rope, and the other end of the steel wire rope is connected to a speed reduction mechanism of the force feedback devices; the other end of the spring is connected with one end of another steel wire rope, and the other end of the steel wire rope is fixed on a spring fixing installation surface on a driven wheel of the base mechanism. The method has the advantages that: the spring and the fixed pulley are arranged on a spring fixing mounting surface on the driven wheel of the base mechanism instead of a large arm mechanism or a small arm mechanism of the force feedback device, so that the inertia of the large arm mechanism or the small arm mechanism of the force feedback device is reduced, and the mutual interference of a steel wire rope and the large arm mechanism or the small arm mechanism at certain positions is avoided. A mathematical model is established for the zero free length spring gravity compensation method, and the method can realize complete gravity compensation.
Disclosure of Invention
The invention discloses a zero free length spring gravity compensation method of force feedback equipment, aiming at the problems of the existing spring gravity compensation technology, which is used for performing gravity compensation on the force feedback equipment. The gravity compensation device comprises a base mechanism, a base speed reduction mechanism, a base pulley, a fixed pulley, a spring fixing and mounting surface, a fixed pulley, a spring fixing and mounting surface, a spring fixing.
The invention is realized by the following technical scheme.
The invention is characterized by comprising the following steps:
(1) one end of a gravity compensation spring of the large arm is connected to a spring fixing mounting surface on a driven wheel of the base speed reducing mechanism, and the other end of the gravity compensation spring is connected to a joint point of a reverse extension line of the large arm and the driven wheel edge on the driven wheel of the large arm speed reducing mechanism through a steel wire rope and a fixed pulley, so that the gravity compensation of the zero free length spring of the large arm mechanism is realized;
(2) one end of a gravity compensation spring of the small arm is connected to a spring fixing mounting surface on a driven wheel of the base speed reducing mechanism, and the other end of the gravity compensation spring is connected to a joint point of the edge of the driven wheel of the small arm speed reducing mechanism through a steel wire rope and a fixed pulley, so that the gravity compensation of the spring with the zero free length of the small arm mechanism is realized.
The invention fully considers the influence of the radius length and the installation position of the fixed pulley on the gravity compensation, establishes a mathematical model for the zero free length spring gravity compensation mode, and theoretically proves that the spring gravity compensation mode can realize complete gravity compensation on the force feedback equipment.
The invention has the advantages that: the spring and the fixed pulley are arranged on the fixed mounting surface of the spring on the driven wheel of the base mechanism of the force feedback device instead of the large arm mechanism or the small arm mechanism of the force feedback device, so that the inertia of the large arm mechanism or the small arm mechanism of the force feedback device is reduced, and the mutual interference of a steel wire rope and the large arm mechanism or the small arm mechanism at certain positions is avoided. In addition, the method also fully considers the influence of the radius length and the installation position of the fixed pulley on gravity compensation, establishes a mathematical model for the zero free length spring gravity compensation mode, and proves that the spring gravity compensation method can realize complete gravity compensation on the force feedback equipment.
Drawings
FIG. 1 is a diagram of the spring gravity compensation connection mechanism of the present invention.
In the figure: the device comprises a base 1, a base deceleration driven wheel 2, a base deceleration driving wheel 3, a direct current motor 4, a base rotating shaft 5, a large arm mechanism 6, a large arm deceleration driven wheel 7, a large arm gravity compensation spring 9, a fixed pulley 10, a small arm mechanism 13, a small arm deceleration driven wheel 14, a small arm deceleration driving wheel 15, a small arm gravity compensation spring 16, a fixed pulley 18, a direct current motor 19, a small arm rotating shaft 20, a small arm deceleration driven wheel rotating shaft 21, a universal joint 22 and a spring fixing and mounting surface.
Fig. 2 is a diagram of the spring gravity compensation connection mechanism rotated 180 clockwise in fig. 1.
In the figure: the device comprises a base 1, a base speed-reducing driven wheel 2, a base rotating shaft 5, a large arm mechanism 7, a large arm speed-reducing driven wheel 8, a large arm speed-reducing driving wheel 10, a fixed pulley 10, a direct current motor 11, a large arm rotating shaft 12, a small arm mechanism 13, a small arm speed-reducing driven wheel 14, a small arm gravity compensation spring 16, a fixed pulley 19, a small arm rotating shaft 17, a universal joint 21 and a spring fixing and mounting surface 22
Fig. 3 is a schematic diagram of zero free length spring gravity compensation of the large arm mechanism of the present invention.
Fig. 4 is a schematic diagram of the zero free length fixed pulley calculation of the present invention.
Detailed Description
The invention will be further explained with reference to the drawings.
The following is described in conjunction with the accompanying figures 1-4: as shown in fig. 1 and 2, the force feedback device is a serial link mechanism having 6 rotational joints, similar to a human arm, and the main components are: the device comprises a base 1, a base deceleration driven wheel 2, a base deceleration driving wheel 3, a direct current motor 4, a base rotating shaft 5, a large arm mechanism 6, a large arm deceleration driven wheel 7, a large arm deceleration driving wheel 8, a large arm gravity compensation spring 9, a fixed pulley 10, a direct current motor 11, a large arm rotating shaft 12, a small arm mechanism 13, a small arm deceleration driven wheel 14, a small arm deceleration driving wheel 15, a small arm gravity compensation spring 16, a fixed pulley 17, a direct current motor 18, a small arm rotating shaft 19, a small arm deceleration driven wheel rotating shaft 20, a universal joint 21, a spring fixing and mounting surface 22 and the like.
As shown in fig. 1 and fig. 2, the large arm mechanism 6, the large arm deceleration driven wheel 7, the large arm deceleration driving wheel 8, the large arm gravity compensation spring 9, the fixed pulley 10, the dc motor 11, the large arm rotating shaft 12, the small arm mechanism 13, the small arm deceleration driven wheel 14, the small arm deceleration driving wheel 15, the small arm gravity compensation spring 16, the fixed pulley 17, the dc motor 18, the small arm rotating shaft 19, the small arm deceleration driven wheel rotating shaft 20, the universal joint 21, the spring fixing and mounting surface 22, and the like are all mounted on the base deceleration driven wheel 2 through a bracket and rotate around the base rotating shaft 5 together with the base deceleration driven wheel 2.
As shown in fig. 1 and 2, the base deceleration driving wheel 3 is nested on the dc motor 4, and when the base dc motor 4 drives the base deceleration driving wheel 3, the two rotate coaxially. The driving wheel 3 of the base speed reducing mechanism drives the base speed reducing driven wheel 2 through a steel wire rope. The seat slows down and rotates around base pivot 5 from driving wheel 2 to through the wire rope transmission, drive big arm mechanism 6, forearm mechanism 13 and universal joint 21 and all rotate around base pivot 5, thereby make the force feedback equipment can produce the feedback force, the base slows down and calculates the acquisition from the photoelectric encoder on 2 turned angle of driving wheel through direct current motor 4.
As shown in fig. 1 and 2, the large-arm deceleration driving wheel 8 is nested on the rotating shaft of the dc motor 11, and when the dc motor 11 drives the large-arm deceleration driving wheel 8, the two rotate coaxially. The big arm deceleration driving wheel 8 drives the big arm deceleration driven wheel 7 through a steel wire rope. The large arm speed reduction driven wheel 7 drives the large arm mechanism 6, the large arm mechanism and the large arm speed reduction driven wheel both rotate around the large arm rotating shaft 12, so that the large arm mechanism 6 can generate feedback force, and the rotating angle of the large arm mechanism 6 is obtained through calculation of a photoelectric encoder on the direct current motor 11. One end of the large-arm gravity compensation spring 9 is connected to a spring fixing mounting surface 22 on the base deceleration driven wheel 2, and the other end of the large-arm gravity compensation spring is connected to the tail end of the large-arm deceleration driven wheel 7 through a steel wire rope and a fixed pulley 10 and used for realizing spring gravity compensation of the large-arm mechanism 1.
As shown in fig. 1 and 2, the small arm deceleration driving wheel 15 is nested on the rotating shaft of the dc motor 18, and when the dc motor 18 drives the small arm deceleration driving wheel 15, the two rotate coaxially. The small arm speed reduction driving wheel 15 drives the small arm speed reduction driven wheel 14 through a steel wire rope. The small arm speed reducing driven wheel 14 rotates around a small arm speed reducing driven wheel rotating shaft 20 and drives the small arm mechanism 13 to rotate around a small arm rotating shaft 19 through transmission of a steel wire rope, so that the small arm mechanism 13 can generate feedback force, and the rotating angle of the small arm mechanism 13 is measured through a photoelectric encoder on the direct current motor 18. The universal joint 21 is installed at the tail end of the small arm mechanism 13, the gravity center of the universal joint 21 is concentrated on the tail end of the small arm mechanism 13, the universal joint 21 is composed of three passive rotary joints, the axes of the three rotary joints are perpendicular to each other, and the rotation angles are measured through respective angle potentiometers. One end of the small arm gravity compensation spring 16 is connected to a spring fixing mounting surface 22 on the base speed reduction driven wheel 2, and the other end of the small arm gravity compensation spring is connected to the tail end of the small arm speed reduction driven wheel 14 through a steel wire rope and a fixed pulley 17, so that the gravity compensation of the small arm mechanism 13 and the universal joint 21 is realized.
For ease of analysis, the zero free length spring gravity compensation method employed in fig. 1 and 2 for the large arm mechanism 6 is depicted schematically in fig. 3. Assume that the large arm mechanism 6 uses a link OO1Indicating, connecting-rod OO1The gravity moment is T ═ Bcos θ. The large arm rotating shaft 12 is represented by O, the stiffness coefficient of the large arm gravity compensation spring 9 is K, the length of the arm OI of the moment generated by the stretching force of the spring to the O is h, and the pulling force of the spring is FsMoment of Ts＝Fsh. Connecting rod OO1Corner ∠ O of1The length r of the radius of the large arm deceleration driven wheel 7 is r, ∠ ION ∠ FQP is θ1∠ QON theta, OG length equals rsin theta, QG length equals rcos theta, one end of the spring is fixed at M, the other end is connected with the wire rope and horizontally tangent to the fixed pulley R point, the other end of the wire rope is fixed on the driven pulley Q point of the large arm speed reducing mechanism and extends to the fixed pulley to intersect the fixed pulley P point, and the Q point is OO1The intersection of the reverse extension line of the driven wheel and the outer diameter of the driven wheel ring. The fixed pulley 10 is a lower disk of FIG. 4 with a center O as shown in FIG. 43Radius length of r', O0The point is a fixed supporting point of the fixed pulley, and the distance from the fixed pulley to the circle center is l and OO0Point W in the figure is the intersection of QP and FM extending tangentially to the fixed pulley, ∠ QWF ∠ PO3E＝β。
For convenience of countingThe pulley portion of fig. 3 is redrawn in fig. 4. As shown in the left drawing of fig. 4, at this time, the link OO1And OO0At the time of coincidence, the gravity moment T — Bcos θ is equal to 0. To ensure that the zero free length spring is gravity compensated, the spring extension should be equal to the free length. Thus, the spring, the fixed pulley and the steel wire rope are combined to form a zero free length spring gravity compensation mode. From the left image of fig. 4, the arc length between the wire ropes QR and QP length plus PR is found:
connecting rod OO1And OO0When the two are not overlapped, as shown in the right diagram of FIG. 4, ∠ QWF is ∠ PO3E- β, O when the point Q is at any point3E has a length r 'cos β equal to the length ER equal to l-r' cos β, so QD has a length a-rsin θ -l + r 'cos β and a length rcos θ -r' sin β, where in Δ QDP the length of QP is:
the QR length of the wire rope is:
therefore, the spring has a tensile length of:
ΔQR＝QR-QR0(4)
the tension of the spring is:
Fs＝KΔQR(5)
the moment of the spring is:
Ts＝KΔQRh (6)
wherein,
h＝rcos(θ-θ1) (7)
using the QD length, DP length, and QP length found, one can find:
in order to fully compensate the spring tension moment for the gravity moment T of the link, Bcos θ, the moment generated by the spring to compensate the gravity should be equal to T, Bcos θ, so the following equation holds:
Bcosθ＝KΔQRh＝KrΔQRcos(θ-θ1) (10)
substituting equations (1), (3), (8) and (9) into (10) yields a spring having a stiffness coefficient K equal to:
wherein, phi ═ (QP + r' β -QR)0)/QP，a′＝a-l+r′cosβ，u′＝r′sinβ。
With respect to equation (11), if l ═ r' is 0 and a ═ r is then the center O of the fixed pulley in fig. 33And O0The coincidence is complete. In order to guarantee a zero free length spring for gravity compensation, there must be: when the connecting rod OO1And OO0When the spring is overlapped, i.e., the gravity moment T ═ Bcos θ is equal to 0, the spring is stretched to a length equal to the free length, i.e., the Q point and O0The point coinciding with the point, i.e. QO0The length is equal to 0. Thus, the combination of the spring, the fixed pulley and the steel wire rope forms a complete zero free length springIn the gravity compensation mode, the stiffness coefficient K of the spring is constant:
the large arm mechanism and the small arm mechanism of the force feedback device need gravity compensation, but the compensation principle of the large arm mechanism and the small arm mechanism is the same. Therefore, the principle of spring compensation of the large arm mechanism is theoretically analyzed, and the principle of spring compensation of the small arm mechanism is similar to the principle of spring compensation of the large arm mechanism, and only the parameters of the small arm mechanism need to be changed.
Through the above mathematical derivation, it is proven that the novel zero-length spring compensation is theoretically completely capable of achieving complete gravity compensation of the force feedback device.
In the actual design process, if a is kept equal to the radius r of the reduction mechanism, the support length l and the radius r' of the fixed pulley are very small, and the stiffness coefficient K of the spring can be made almost constant, which can be realized in the actual production process. Therefore, the method is simple and easy to implement.
In addition, the spring and the steel wire rope of the method are fixed on the spring fixing mounting surface on the driven wheel of the base mechanism of the force feedback equipment instead of the connecting rod of the operator, so that the gravity and inertia of the force feedback equipment during operation are not increased, interference between the rod and the rod is avoided, and the defect of a common zero free length spring is avoided.
Claims (1)
1. A zero free length spring gravity compensation method based on force feedback equipment is characterized by comprising the following steps:
(1) one end of a large-arm gravity compensation spring is connected to a spring fixing mounting surface on a driven wheel of a base speed reducing mechanism, and the other end of the large-arm gravity compensation spring is connected to a joint point of a reverse extension line of a large arm and the driven wheel edge on the driven wheel of the large-arm speed reducing mechanism through a steel wire rope and a fixed pulley, so that zero free length spring gravity compensation of the large-arm mechanism is realized; connecting rod OO for large arm mechanism1Indicating, connecting-rod OO1The gravity moment is T ═ B cos theta; big arm rotatingThe axis is represented by O, a horizontal line NL is formed by a point O, and points N and L are two points on the horizontal line respectively; the stiffness coefficient of the large-arm gravity compensation spring is K, the length of a force arm OI of a stretching force of the large-arm gravity compensation spring to a moment generated by O is h, wherein I is a point I, a perpendicular line is drawn from the point O and is intersected with the extension line of PQ, and the intersection point is a point I, so that the tension of the large-arm gravity compensation spring is FsMoment of Ts＝Fsh; connecting rod OO1Corner ∠ O of1OL ═ θ; through O0Making a horizontal line from the point Q, making a vertical line from the point Q to intersect with the horizontal line, wherein the intersection point is F; making a vertical line from the point P to be vertical to QF, wherein the intersection point is D; passing through O point, O3Dot and O0The point is a straight line, a perpendicular line from the point Q is crossed with the straight line at the point G, a perpendicular line from the point P is crossed with the straight line at the point E, and the length r, ∠ ION (∠ FQP) for the radius of the large arm deceleration driven wheel is r1∠ QON theta, OG length equals rsin theta, QG length equals rcos theta, one end of large arm gravity compensation spring is fixed at M, another end is connected with wire rope and tangent horizontally and crossed at fixed pulley R point, another end of wire rope is fixed on driven wheel Q point of large arm speed reducing mechanism and extended to fixed pulley and crossed with fixed pulley P point, Q point is OO1The intersection of the reverse extension line and the outer diameter of the driven wheel ring; the circle center of the fixed pulley is O3Radius length of r', O0The point is a fixed supporting point of the fixed pulley, and the distance from the fixed pulley to the circle center is l and OO0A point W is the intersection point of QP and FM after QP is tangent to the fixed pulley, ∠ QWF ∠ PO3E＝β；
Connecting rod OO1And OO0When the two phases are overlapped, the gravity moment T is equal to B cos theta and is equal to 0; in order to ensure that the large-arm gravity compensation spring with zero free length carries out gravity compensation, at the moment, the extension length of the large-arm gravity compensation spring is equal to the free length; thus, the large-arm gravity compensation spring, the fixed pulley and the steel wire rope are combined to form a gravity compensation mode of the large-arm gravity compensation spring with zero free length; the length between the steel wire ropes QR is calculated as the length of the arc between QP and PR:
connecting rod OO1And OO0When the two steel wire ropes are overlapped, the gravity moment T is equal to B cos theta and is equal to 0, and the length of the steel wire rope QR at the moment is recorded as QR0；
Connecting rod OO1And OO0When not coincident, ∠ QWF is ∠ PO3E- β, O when the point Q is at any point3E has a length r 'cos β equal to the length ER equal to l-r' cos β, so QD has a length a-r sin θ -l + r 'cos β and a length rcos θ -r' sin β, where in Δ QDP the length of QP is:
the QR length of the wire rope is:
therefore, the extension length of the large arm gravity compensation spring is as follows:
ΔQR＝QR-QR0(4)
the tension of the large-arm gravity compensation spring is as follows:
Fs＝KΔQR(5)
the moment of the large-arm gravity compensation spring is as follows:
Ts＝KΔQRh (6)
wherein,
h＝r cos(θ-θ1) (7)
using the QD length, DP length, and QP length found, one can find:
in order to fully compensate the tension moment of the large-arm gravity compensation spring for the gravity moment T of the connecting rod, which is equal to B cos θ, the moment for compensating the gravity generated by the large-arm gravity compensation spring should be equal to T, which is equal to B cos θ, so the following equation holds:
B cosθ＝KΔQRh＝KrΔQRcos(θ-θ1) (10)
substituting equations (1), (3), (8) and (9) into (10) can determine that the stiffness coefficient K of the large-arm gravity compensation spring is equal to:
wherein, phi ═ (QP + r' β -QR)0)/QP，a′＝a-l+r′cosβ，u′＝r′sinβ；
In equation (11), if l ═ r' is 0 and a ═ r is the center O of the fixed pulley3And O0The overlapping is complete; in order to guarantee zero free length spring gravity compensation of the large arm mechanism, there must be: when the connecting rod OO1And OO0When the two springs are overlapped, namely the gravity moment T is equal to B cos theta and is equal to 0, the stretching length of the large-arm gravity compensation spring is equal to the free length, namely the point Q and the point O0The point coinciding with the point, i.e. QO0The length is equal to 0; like this, big arm gravity compensation spring just constitutes complete zero free length spring gravity compensation mode with fixed pulley and wire rope combine together, and big arm gravity compensation spring's rigidity coefficient K is the constant:
(2) one end of a gravity compensation spring of the small arm is connected to a spring fixing mounting surface on a driven wheel of the base speed reducing mechanism, and the other end of the gravity compensation spring of the small arm is connected to a joint point of the edge of the driven wheel of the small arm speed reducing mechanism through a steel wire rope and a fixed pulley, so that the gravity compensation of the zero free length spring of the small arm mechanism is realized; for gravity compensation of the small arm mechanism, parameters of the small arm mechanism need to be changed.
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| CN110404157A (en) * | 2019-08-03 | 2019-11-05 | 安徽工程大学 | A kind of robot sinusoidal elastic force amplifying moment compensation device and method |
| CN111216129B (en) * | 2020-01-07 | 2023-03-21 | 华南理工大学 | Active-passive combined series-parallel force feedback equipment gravity compensation method |
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