CN105619389A - Symmetrical parallel mechanism without singularities - Google Patents

Abstract

The invention discloses a symmetrical parallel mechanism without singularities. The symmetrical parallel mechanism without the singularities comprises a movable platform, a fixed platform used as a frame, and four kinematic chains connecting the movable platform and the fixed platform, wherein the four kinematic chains comprise a properly constrained chain connecting the central position of the movable platform and the central position of the fixed platform, and three identical kinematic branched chains; the three kinematic branched chains are symmetrically distributed about the centre of the properly constrained chain; the parallel mechanism has three degrees of freedom and four degrees of freedom respectively through addition or no addition of a revolute pair on the properly constrained chain; and the parallel mechanisms with the two degrees of freedom both have the characteristics of symmetrical structure and no singularities. The symmetrical parallel mechanism without the singularities, which is disclosed by the invention, can be applied to the fields of motion simulators, telescope secondary mirror support mechanisms, mechanical wrists, coordinate measuring machines, micro-operation robots, machine tool spindle heads and the like, and has a wide application prospect.

Description

A kind of symmetric parallel mechanism without Singularity

Technical field

The invention belongs to machinery manufacturing technology field, it relates to a kind of symmetric parallel mechanism without Singularity.

Background technology

Compared to serial mechanism, parallel institution has that rigidity is big, supporting capacity height, precision height and the advantage such as inverse kinematic is easy, is thus applied widely in industrial robot, mechanical manufacturing field. And minority carrier generation lifetime (parallel institution that degree of freedom is less than 6) has the features such as structure is simple, cost is low, kinematics solution is relatively simple, the 3-freedom parallel mechanism that wherein type is moved in two rotations one is a class configuration extremely important in parallel institution. Since HUNT1983 proposes 3-RPS parallel institution, two rotate one moves type 3-freedom parallel mechanism for many fields, as supported the fields such as mechanism, pose_adjuster, motion simulation device, mechanical wrist, measurement of coordinates machine, micro-manipulating robot based on the Z3 main tapping of 3-PRS parallel institution, astronomical telescope secondary mirror. But, there is the problem of Singularity in existing 3-freedom parallel mechanism, makes mechanism path planning more difficult. Four-freedom parallel mechanism has three rotations one and moves the relatively less of symmetrical configurations, as 4-SPS/PS mechanism exists Singularity, and there is the characteristic of tight coupling so that trajectory planning and control comparatively difficulty.

Summary of the invention

It is an object of the invention to provide a kind of symmetric parallel mechanism without Singularity, this parallel institution have symmetrical configuration, big containing Singularity, working space, supporting capacity by force, just simple against solution form, drive pair to be positioned on fixed platform, the simple feature of type of drive, this parallel institution can be applied in motion simulation device, visual telescope secondary mirror supports mechanism, mechanical wrist, measurement of coordinates machine, micro-manipulating robot, machine tool chief axis head.

The technical solution adopted in the present invention is, a kind of symmetric parallel mechanism without Singularity, comprise moving platform, as the fixed platform of frame and four kinematic links of connection moving platform and fixed platform, article four, movement branched chain comprises the proper constraint chain and three complete identical movement branched chain that connect moving platform central position and fixed platform central position, article three, complete identical movement branched chain comprises the hydro-cylinder being fixedly connected with fixed platform, 3 hydro-cylinders are connected with piston rod by cylinder secondary A respectively, 3 piston rods are connected with annular element by rotating secondary A respectively, 3 annular elements are connected with sliding bar by cylinder secondary B respectively, by rotating, secondary B is connected the sliding bar one end of every root with moving platform center, the sliding bar the other end is secondary by rotating to be connected with roller, roller contacts with the raceway being arranged on moving platform, the axis of cylinder secondary A described in each and the axis of rotation secondary A corresponding with it are orthogonal, the axis of rotation secondary A described in each and the axis of cylinder secondary B corresponding with it are orthogonal, the axis of cylinder secondary B described in each and the axis of rotation secondary B corresponding with it are orthogonal, article three, the axis coaxle of the rotation secondary B in movement branched chain.

The feature of the present invention is also,

The hydro-cylinder that proper constraint chain comprises with fixed platform central position is fixedly connected with, hydro-cylinder is connected with piston rod one end by moving sets, and the piston rod the other end is connected with Hooke's hinge, and Hooke's hinge is connected with moving platform central position.

The hydro-cylinder that proper constraint chain comprises with fixed platform central position is connected by rotating secondary C, hydro-cylinder is connected with piston rod one end by moving sets, and the piston rod the other end is connected with Hooke's hinge, and Hooke's hinge is connected with moving platform central position.

The central point of Hooke's hinge is the intersection point of axis and the moving platform place plane rotating secondary B, rotates axis and the moving platform normal parallel of secondary B.

The spacing of adjacent two cylinder secondary A is equal, and moving sets is positioned at the point midway of the equilateral triangle formed taking the position of cylinder secondary A as summit, and the axis of 3 cylinder secondary A is mutually parallel with the axis of moving sets.

The type of drive of parallel institution be in electric, pneumatic, hydraulic pressure any one.

The useful effect of the present invention is, the cylinder secondary A in three movement branched chain is secondary as the driving of mechanism, and drive form is simple, and avoids driving mechanism and be positioned at other positions of movement branched chain and introduce relatively Great inertia; In addition contain proper constrained branched chain due to mechanism and can obtain high-precision motion further by proper constrained branched chain adds the method for redundant drive, this parallel institution is unrestricted along the rotation scope in the plane of moving platform place, can continuously rotate by complete cycle, it is applicable to middle low speed rotation occasion; Mechanism's partly decoupled simultaneously, symmetrical configuration. The parallel institution of the present invention have better simply just inverse separate, without unusual bit-type, working space is big, supporting capacity is strong, there is good motion characteristics, drive form is simple, it is possible to be applied in motion simulation device, visual telescope secondary mirror support mechanism, mechanical wrist, measurement of coordinates machine, micro-manipulating robot, machine tool chief axis head.

Accompanying drawing explanation

Fig. 1 is the schematic diagram of mechanism of the first embodiment of a kind of symmetric parallel mechanism without Singularity of the present invention;

Fig. 2 is the structural representation of a kind of symmetric parallel mechanism without Singularity of the present invention;

Fig. 3 is the structural representation of moving platform in a kind of symmetric parallel mechanism without Singularity of the present invention;

The schematic diagram of mechanism of the 2nd kind of embodiment of a kind of symmetric parallel mechanism without Singularity of Fig. 4 the present invention.

In figure, 1. fixed platform, 2. slides bar, 3. piston rod, 4. roller, 5. moving platform, 6. annular element, 7. hydro-cylinder, 8. cylinder secondary A, 9. rotates secondary A, 10. cylinder secondary B, 11. rotation secondary B, 12. Hooke's hinges, 13. moving sets, 14. rotation secondary C.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.

Embodiment 1

A kind of symmetric parallel mechanism without Singularity of the present invention, as shown in Figures 1 and 2, comprise moving platform 5, as the fixed platform 1 of frame and four movement branched chain of connection moving platform and fixed platform, article four, movement branched chain comprises the proper constraint chain and three complete identical movement branched chain that connect moving platform 5 central position and fixed platform 1 central position, article three, complete identical movement branched chain comprises the hydro-cylinder 7 being fixedly connected with fixed platform 1, 3 hydro-cylinders 7 are connected with piston rod 3 by cylinder secondary A8 respectively, 3 piston rods 3 are connected with annular element 6 by rotating secondary A9 respectively, as shown in Figure 3, 3 annular elements 6 are connected with sliding bar 2 by cylinder secondary B10 respectively, by rotating, secondary B11 is connected sliding bar 2 one end of every root with moving platform 5 central position, sliding bar 2 the other end is secondary by rotating to be connected with roller 4, roller 4 contacts with the raceway being arranged on moving platform 5, the axis of each cylinder secondary A8 and the axis of rotation secondary A9 corresponding with it are orthogonal, the axis of each rotation secondary A9 and the axis of cylinder secondary B10 corresponding with it are orthogonal, the axis of each cylinder secondary B10 and the axis of rotation secondary B11 corresponding with it are orthogonal, the hydro-cylinder 7 that proper constraint chain comprises with fixed platform 1 central position is fixedly connected with, hydro-cylinder 7 is connected with piston rod 3 one end by moving sets 13, piston rod 3 the other end is connected with Hooke's hinge 12, Hooke's hinge 12 is connected with moving platform 5 central position, article three, the axis coaxle of the rotation secondary B11 in movement branched chain, the intersection point of the axis and moving platform 5 place plane that rotate secondary B11 is the central point of Hooke's hinge 12, rotate axis and moving platform 5 normal parallel of secondary B11, the spacing homogeneous phase etc. of adjacent two cylinder secondary A, moving sets 13 is positioned at the point midway of the equilateral triangle formed taking the position of cylinder secondary A8 as summit, the axis of cylinder secondary A8 is mutually parallel with the axis of moving sets 13, the type of drive of parallel institution is electric, pneumatic, in hydraulic pressure any one.

The first embodiment of a kind of lower-mobility symmetric parallel mechanism without Singularity of the present invention, it provides a kind of two rotate the parallel institution of the three degree of freedom that moves, and the kinematics of this parallel institution against solution is:

$z_1=z+\frac{1}{2}a(\sec \mathrm{\α}\·tan\mathrm{\β}+\sqrt{3}tan\mathrm{\α})$

$z_2=z+\frac{1}{2}a(\sec \mathrm{\α}\·tan\mathrm{\β}-\sqrt{3}tan\mathrm{\α})$

z₃=z-asec �� tan ��

The forward kinematics solution of above-mentioned parallel institution is:

$\mathrm{\α}=arctan\left(\frac{z_1-z_2}{\sqrt{3}\·a}\right)$

$\mathrm{\β}=arctan\left(\frac{z_1+z_2-2z_3}{\sqrt{3{(z_2-z_1)}^2+9a^2}}\right)$

Z=(z₁+z₂+z₃)/3

Kinematics is asked against solution and leads that to obtain mechanism Jacobian matrix J as follows:

$J=\left[\begin{array}{ccc}\frac{a}{2}\sec \mathrm{\α}(tan\mathrm{\α}\·tan\mathrm{\β}+\sqrt{3}\sec \mathrm{\α})& \frac{a}{2}\sec \mathrm{\α}\·{\sec }^2\mathrm{\β}& 1\\ \frac{a}{2}\sec \mathrm{\α}(tan\mathrm{\α}\·tan\mathrm{\β}-\sqrt{3}\sec \mathrm{\α})& \frac{a}{2}\sec \mathrm{\α}\·{\sec }^2\mathrm{\β}& 1\\ -a\·tan\mathrm{\α}\·\sec \mathrm{\α}\·tab\mathrm{\β}& a\·{\mathrm{sec\αsec}}^2\mathrm{\β}& 1\end{array}\right]$

Various middle z above₁��z₂��z₃The bar being respectively on three driving side chains as the cylinder secondary A driven is long; Z is the position of moving platform true origin z-axis under fixed platform coordinate, ��, ��, �� are moving platform pose (the i.e. X-axis rotation alpha angle of the first moving platform system of coordinates of moving platform that moving platform XYZ type Eulerian angles represent, under new system of coordinates, Y-axis turns �� angle again, then turns �� angle around the new system of coordinates Z axle obtained); A represents the slant range of cylinder secondary A place axis to moving sets place axis.

By the Jacobian matrix that the motion analysis of above-mentioned parallel institution is tried to achieve, it is possible to the motion characteristics of analysis institution: for this mechanism,Wherein | �� | < 90 ��, | �� | < 90 ��, so det (J) �� 0, there is not Singularity in this mechanism.

Embodiment 2

A kind of symmetric parallel mechanism without Singularity of the present invention, as shown in Figures 2 and 4, comprise moving platform 5, as the fixed platform 1 of frame and four movement branched chain of connection moving platform 5 and fixed platform 1, article four, movement branched chain comprises the proper constraint chain and three complete identical movement branched chain that connect moving platform 5 central position and fixed platform 1 central position, article three, complete identical movement branched chain comprises the hydro-cylinder 7 being fixedly connected with fixed platform 1, 3 hydro-cylinders 7 are respectively by cylinder secondary A8 and piston rod 3, 3 piston rods 3 are connected with annular element 6 by rotating secondary A9 respectively, as shown in Figure 3, 3 annular elements 6 are connected with sliding bar 2 by cylinder secondary B10 respectively, by rotating, secondary B11 is connected sliding bar 2 one end of every root with moving platform 5 central position, sliding bar 2 the other end is secondary by rotating to be connected with roller 4, roller 4 contacts with the raceway being arranged on moving platform 5, the axis of each cylinder secondary A8 and the axis of rotation secondary A9 corresponding with it are orthogonal, the axis of each rotation secondary A9 and the axis of cylinder secondary B10 corresponding with it are orthogonal, the axis of each cylinder secondary B10 and the axis of rotation secondary B11 corresponding with it are orthogonal, the hydro-cylinder 7 that proper constraint chain comprises with fixed platform 1 central position is connected by rotating secondary C14, hydro-cylinder 7 is connected with piston rod 3 one end by moving sets 13, piston rod 3 the other end is connected with Hooke's hinge 12, Hooke's hinge 12 is connected with moving platform 5 central position, the hydro-cylinder 7 that proper constraint chain comprises with fixed platform 1 central position is connected by rotating secondary C14, hydro-cylinder 7 is connected with piston rod 3 one end by moving sets 13, piston rod 3 the other end is connected with moving platform 5 central position by Hooke's hinge 12, article three, the axis coaxle of the rotation secondary B11 in movement branched chain, the intersection point of the axis and moving platform 5 place plane that rotate secondary B11 is the central point of Hooke's hinge 12, rotate axis and moving platform 5 normal parallel of secondary B11, distance between adjacent two cylinder secondary A8 is all equal, moving sets 13 is positioned at the point midway of the equilateral triangle formed taking the position of cylinder secondary A8 as summit, the axis of cylinder secondary A8 is mutually parallel with the axis of moving sets 13, the type of drive of parallel institution is electric, pneumatic, in hydraulic pressure any one.

2nd kind of embodiment of a kind of lower-mobility symmetric parallel mechanism without Singularity of the present invention, secondary C14 is rotated by 3 cylinder secondary A8 and 1, thus make mechanism obtain four degree of freedom, provide the parallel institution that a kind of three rotate the four-degree-of-freedom that moves, moving platform more than 5 goes out a degree of freedom �� rotated around its place plane, and corresponding driving is rotated the rotational angle theta of secondary C14 and is:

��=arctan (cos �� sec �� tan ��+sin �� tan ��)

Upper formula is the inverse solution of one, this parallel institution mechanism, and corresponding just solution is:

$\mathrm{\&gamma;}=arctan\left(\frac{1}{m}\right(tan\mathrm{\&theta;}\&CenterDot;\left({\left(z_2-z_1\right)}^2+3a^2\right)+\frac{1}{\sqrt{3}}\left(z_1-z_2\right)\&CenterDot;\left(z_1+z_2-2z_3\right)\left)\right)$

This four-freedom parallel mechanism is sought Jacobian matrix G:

$\det \left(G\right)=\frac{3\sqrt{3}{a}^2({\tan }^2\mathrm{\&gamma;}+1)}{2{\cos }^4\mathrm{\&alpha;}\&CenterDot;\cos \mathrm{\&beta;}({\tan }^2\mathrm{\&gamma;}+2\tan \mathrm{\&alpha;}\sin \mathrm{\&beta;}\tan \mathrm{\&gamma;}+{\sec }^2{\mathrm{\&alpha;cos}}^2\mathrm{\&beta;}+{\tan }^2{\mathrm{\&alpha;sin}}^2\mathrm{\&beta;})}\&NotEqual;0$

Also there is not unusual bit-type.

The parallel institution of above two kinds of embodiment gained has continuous motion characteristics, moving platform can any boning out realize rotating continuously in its working space in the plane of moving platform place, and moving platform can rotate continuously around any fixed-point implementation in the plane of moving platform place, mechanism can also carry out continuous moving along the guide passage direction of moving sets in the proper constraint chain in centre, two kinds of parallel institutions have bigger working space, mechanism's moving platform can rotate around the proper constrained branched chain end Hooke's hinge at center, and on proper constrained branched chain, moving sets axis direction is moved.

Claims (6)

1. the symmetric parallel mechanism without Singularity, comprise moving platform (5), as the fixed platform (1) of frame and four movement branched chain of connection moving platform (5) and fixed platform (1), article four, movement branched chain comprises the proper constraint chain and three complete identical movement branched chain that connect moving platform (5) central position and fixed platform (1) central position, article three, complete identical movement branched chain comprises the hydro-cylinder (7) being fixedly connected with fixed platform (1), 3 hydro-cylinders (7) are connected with piston rod (3) by cylinder secondary A (8) respectively, 3 piston rods (3) are connected with annular element (6) by rotating secondary A (9) respectively, 3 annular elements (6) are connected with sliding bar (2) by cylinder secondary B (10) respectively, by rotating, secondary B (11) is connected sliding bar (2) one end of every root with moving platform (5) center, sliding bar (2) the other end is secondary by rotating to be connected with roller (4), roller (4) contacts with the raceway being arranged on moving platform (5), the axis of cylinder secondary A (8) described in each and the axis of rotation secondary A (9) corresponding with it are orthogonal, the axis of rotation secondary A (9) described in each and the axis of cylinder secondary B (10) corresponding with it are orthogonal, the axis of cylinder secondary B (10) described in each and the axis of rotation secondary B (11) corresponding with it are orthogonal, article three, rotation secondary B (11) axis coaxle of movement branched chain.

2. a kind of symmetric parallel mechanism without Singularity according to claim 1, it is characterized in that, described proper constraint chain comprises the hydro-cylinder (7) being fixedly connected with fixed platform (1) central position, hydro-cylinder (7) is connected with piston rod (3) one end by moving sets (13), piston rod (3) the other end is connected with Hooke's hinge (12), and Hooke's hinge (12) is connected with moving platform (5) central position.

3. a kind of symmetric parallel mechanism without Singularity according to claim 1, it is characterized in that, the hydro-cylinder (7) that described proper constraint chain comprises with fixed platform (1) central position is connected by rotating secondary C (14), hydro-cylinder (7) is connected with piston rod (3) one end by moving sets (13), piston rod (3) the other end is connected with Hooke's hinge (12), and Hooke's hinge (12) is connected with moving platform (5) central position.

4. a kind of symmetric parallel mechanism without Singularity according to Claims 2 or 3, it is characterized in that, the central point of described Hooke's hinge (12) is the intersection point of axis and moving platform (5) the place plane rotating secondary B (11), rotates axis and moving platform (5) normal parallel of secondary B (11).

5. a kind of symmetric parallel mechanism without Singularity according to Claims 2 or 3, it is characterized in that, the spacing homogeneous phase etc. of described adjacent two cylinder secondary A (8), moving sets (13) is positioned at the central position of the equilateral triangle formed taking the position of 3 cylinder secondary A (8) as summit, and the axis of 3 cylinder secondary A (8) is mutually parallel with the axis of moving sets (13).

6. a kind of symmetric parallel mechanism without Singularity according to claim 1, it is characterised in that, the type of drive of described parallel institution be in electric, pneumatic, hydraulic pressure any one.