Finite Twist Mapping and its Application to Planar Serial Manipulators with Revolute Joints

Abstract

This paper reviews a method of representing the finite twist motion of a rigid body, and applies this concept to the problem of describing the motion capabilities of planar serial manipulators. In particular, this finite twist representation describes the position and orientation of the end-effector link relative to a defined reference position and orientation. The transformations associated with the joint motions are used to investigate the range of end-effector motion, including the effects of limits of joint travel. The finite twist representations are then extracted from such transformations and presented in an image space so that the motion of the manipulator is fully characterized. Further, the reachable and dexterous workspaces are predicted by the same general means. Examples of planar serial manipulators with two (RR) and three revolute (RRR) joints are given to illustrate the approach.

Keywords

finite twist motion planar serial manipulators workspaces image spaces dexterity

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References

Chasles

Note sur le propriétés générales du système de deux corps semblables entr'eux et placés d'une manière quelconque dans l'espace; et sur le déplacement fini ou infiniment petit d'un corps solide libre. Bull. Sci. Mach., 1830, 14, 321–326.

Kerr

D. R.

Dai

J. S.

Rigid body finite displacements and their finite twist representations. Submitted to Phil. Trans. R. Soc., January 1994.

Baker

J. E.

Waldron

K. J.

Limit positions of spatial linkages via screw system theory. ASME Mechanisms Conference, 1974, paper 74-DET-107 (American Society of Mechanical Engineers, New York).

Gupta

K. C.

Roth

Design considerations for manipulator workspace. Trans. ASME J. Mech. Des., 1981, 103, 776–784.

Kumar

Waldron

K. J.

The dextrous workspace. ASME paper 80-DET-108, 1980.

Davidson

J. K.

Hunt

K. H.

Rigid body location and robot workspaces: some alternative manipulator forms. Trans. ASME J. Mechanisms Transmissions and Automn in Des., 1987, 109(1), 50–60.

Sugimoto

Duffy

Determination of extreme distances of a robot hand. Part 1: a general theory. Trans. ASME J. Mech. Des., July 1981, 103(3), 631–637.

Davidson

J. K.

Pingali

Robot workspace of a tool plane. Part II: computer generation and selected design conditions for dexterity. Trans. ASME J. Mechanism Transmissions and Automn in Des., 1987, 109(1), 61–71.

Yoshikawa

Manipulability of robotic mechanisms. Int. J. of Robotic Res., 1985, 4(2), 3–9.

10.

Sastry

S. S.

Task-oriented optimal grasping by multi-fingered robot hands. IEEE J. Robotics and Automn, February 1988, 4(1), 32–44.

11.

Tsai

M. J.

Chiou

Y. H.

Manipulability of manipulators. Mech. Mach. Theory, 1990, 25(5), 575–585.

12.

Duffy

The fallacy of modern hybrid control theory that is based on ‘orthogonal complements’ of twist and wrench spaces. J. Robotic Systems, 1990, 7(2), 139–144.

13.

Y. K.

Fischer

I. S.

Motion synthesis of mechanisms using constraint manifolds. Proceedings of Twenty-third ASME Mechanisms Conference, Minneapolis, Minnesota 1994, Vol. 70, pp. 441–448 (American Society of Mechanical Engineers, New York).

14.

Normand

J.-M.

A lie group: rotations in quaternion mechanics, 1980 (North-Holland, Oxford).

15.

McKerrow

P. J.

Introduction to robotics, 1991 (Addison-Wesley, New York).

16.

Dai

J. S.

Kerr

D. R.

Analysis and synthesis of frictionless grasping in an image space. Proceedings of Twenty-second ASME Mechanisms Conference, Scottsdale, Arizona 1992, Vol. 45, pp. 283–292 (American Society of Mechanical Engineers, New York).