As shown in this paper, when designing parallel manipulators for tasks involving less than six degrees of freedom, the topology can be laid out by resorting to qualitative reasoning. More specifically, the paper focuses on cases whereby the manipulation tasks pertain to displacements with the algebraic structure of a group. Besides the well-known planar and spherical displacements, this is the case of displacements involving: rotation about a given axis and translation in the direction of the same axis (cylindrical subgroup); translation in two and three dimensions (two- and three-dimensional translation subgroups); three independent translations and rotation about an axis of fixed direction, what is known as the Scho¨nflies subgroup; and similar to the Scho¨nflies subgroup, but with the rotation and the translation in the direction of the axis of rotation replaced by a screw displacement. For completeness, the fundamental concepts of motion representation and groups of displacements, as pertaining to rigid bodies, are first recalled. Finally, the concept of Π-joint, introduced elsewhere, is generalized to two and three degrees of freedom, thereby ending up with the Π2-and the Π3-joints, respectively.

Issue Section:
Technical Papers
Keywords:
manipulator kinematics, common-sense reasoning, topology, product design
Topics:
Design, Displacement, Generators, Kinematics, Manipulators, Rotation, Topology, Robots, Kinematic chains, Algebra, Dimensions, Screws, Degrees of freedom, Robotics, Architecture
1.
Hunt
,
K. H.
,
1983
, “
Structural Kinematics of In-Parallel-Actuated Robot Arms
,”
J. Eng. Mech. Div.
,
105
, pp.
705
–
712
.
2.
Gosselin, C., and Angeles, J., 1987, “The Optimum Kinematic Design of a Spherical Three-Degree-of-Freedom Parallel Manipulator,” Proc. 13th ASME Design Automation Conference, Sept. 27–30, Boston, pp. 111–115.
3.
Craver, W. M., 1989, “Structural Analysis and Design of a Three-Degree-of-Freedom Robotic Shoulder Module,” Master’s Thesis, The University of Texas at Austin, Department of Mechanical Engineering, Austin.
4.
Lee, K. M., and Shah. D. K., 1987, “Kinematic Analysis of a Three-Degree-of-Freedom in Parallel Actuated Manipulators,” Proc. IEEE Int. Conf. Robotics and Automation, Vol. 1, pp. 345–350.
5.
Lee
,
K. M.
, and
Arjuman
,
S.
,
1991
, “
A 3-DOF Micromotion In-Parallel Actuated Manipulator
,”
IEEE Trans. Rob. Autom.
,
7
(
5
), pp.
634
–
640
.
6.
Agrawal, S. K., 1991, “Study of an In-Parallel Mechanism Using Reciprocal Screws,” Proc. 8th World Congress on TMM, Prague, 26–31 Aug. 1991, pp. 405–408.
7.
Pfreundschuh, G. H., Kumar, V., and Sugar, T. H., 1991, “Design and Control of a Three-Degree-of-Freedom In-Parallel Actuated Manipulator,” Proc. IEEE Int. Conf. Robotics and Automation, pp. 1659–1664.
8.
Clavel, R., 1990, Device for the Movement and Positioning of an Element in Space, U. S. Patent No. 4,976,582 of December 11.
9.
Broga˚rdh, T., 2001, Device for Relative Movement of Two Elements, U.S. Patent No. 6,301,988 B1 of October 16.
10.
Herve´, J. M., and Sparacino, F., 1992, “Star, a New Concept in Robotics,” Proc. 3rd Int. Workshop on Advances in Robot Kinematics, September 7–9, Ferrara, pp. 176–183.
11.
Arai, T., Herve´, J. M., and Tanikawa, T., 1996, “Development of 3 DOF Micro Finger,” Proc. IROS’96, November 5–8, Osaka, pp. 981–987.
12.
Company, O., Pierrot, F., Shibukawa, T., and Koji, M., 2001, Four-Degree-of-Freedom Parallel Robot, European Patent EP1084802, March 21.
13.
Herve´
,
J. M.
,
1978
, “
Analyze Structurelle des Me´canismes par Groupes de De´placements
,”
Mech. Mach. Theory
,
13
, pp.
437
–
450
.
14.
Herve´
,
J. M.
,
1999
, “
The Lie Group of Rigid Body Displacements, a Fundamental Tool for Mechanism Design
,”
Mech. Mach. Theory
,
34
, pp.
719
–
730
.
15.
Hartenberg, R. S., and Denavit, J., 1964, Kinematic Synthesis of Linkages, McGraw-Hill Book Company, New York.
16.
Angeles, J., 1982, Spatial Kinematic Chains. Analysis, Synthesis, Optimization, Springer-Verlag, New York.
17.
Macdonald, I. D., 1968, The Theory of Groups, Oxford University Press, London.
18.
Wohlhart
,
K.
,
1991
, “
Der homogene Paralleltrieb-Mechanismus
,”
Mathematica Pannonica
,
2
(
2
), pp.
59
–
76
.
19.
Wohlhart, K., 1992, “Displacement Analysis of the General Spatial Parallelogram Manipulator,” Proc. 3rd International Workshop on Advances in Robot Kinematics, Ferrara, Italy, pp. 104–111.
20.
Dietmaier, P., 1992, “Inverse Kinematics of Manipulators With 3 Revolute and 3 Parallelogram Joints,” Proc. ASME 22nd. Biennial Mechanisms Conference, Sept. 13–16, Scottsdale, Vol. 45, pp. 35–40.
21.
Clavel, R., 1988, “Delta, a Fast Robot with Parallel Geometry,” Proc. 18th Int. Symp. Industrial Robots, Lausanne, pp. 91–100.
22.
Angeles, J., Morozov, A., and Navarro, O., 2000, “A Novel Manipulator Architecture for the Production of SCARA Motions,” Proc. IEEE Int. Conf. Robotics and Automation, San Francisco, pp. 2370–2375. CD-ROM 00CH37065C, April 24–28.
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