In this paper, we introduce a new class of parallel manipulators, called general hybrid parallel manipulators (GHPM). These are modular manipulators that may contain serial subchains as well as subchains of parallel modules, acting in parallel and connecting a base to a common platform. The instantaneous motion of the GHPM is studied by resorting to the theory of screws. In this context, we define the screw-system annihilator to reduce, systematically, the number of unknowns involved to a minimum. The formulation presented here is general and can be applied to most existing parallel manipulators, multifingered hands, multiple coordinated robots and walking machines. To illustrate the basic symbolical and numerical aspects of the proposed procedure, the analyses of the instantaneous kinematics of two hybrid manipulators are included.

1.
Benhabib
B.
,
Zak
G.
, and
Lipton
M. G.
,
1989
, “
A Generalized Kinematic Modeling Method for Modular Robots
,”
J. Robotic Systems
, Vol.
6
, No.
5
, pp.
545
571
.
2.
Charentus, S., and Renaud, M., 1990, “Modeling and Control of a Modular, Redundant Robot Manipulator,” Experimental Robotics I, V. Hayward and O. Khatib, eds., New York, Springer, pp. 508–527.
3.
Cheng
H. H.
,
1994
, “
Real-Time Manipulation of a Hybrid Serial-and-Parallel-Driven Redundant Industrial Manipulator
,”
ASME Journal of Dynamic Systems, Measurement, and Control
, Vol.
116
, pp.
687
701
.
4.
Craig, J. J., 1989, Introduction to Robotics. Mechanics and Control, Addison-Wesley Publishing Co., Reading, MA.
5.
Earl
C. F.
, and
Rooney
J.
,
1983
, “
Some Kinematic Structures for Robot Manipulator Designs
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
, Vol.
105
, pp.
15
22
.
6.
Golub, G. H., and Van Loan, C. F., 1989, Matrix Computations, The Johns Hopkins Univ. Press, Baltimore.
7.
Hayward, V., and Kurtz, R., 1991, “Modeling of a Parallel Wrist Mechanism with Actuator Redundancy,” in Stifter S. and Lenarcˇicˇ, J. (eds.), Advances in Robot Kinematics, Springer-Verlag, Vienna, pp. 444–456.
8.
Huang
C.
, and
Roth
B.
,
1994
, “
Position-Force Synthesis of Closed-Loop Linkages
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
116
, pp.
155
162
.
9.
Hunt, K. H. 1978, Kinematic Geometry of Mechanisms, Clarendon Press, Oxford.
10.
Hunt
K. H.
,
1983
, “
Structural Kinematics of In-Parallel-Actuated Robot-Arms
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
, Vol.
105
, pp.
705
712
.
11.
Kelmar
L.
, and
Khosla
P. K.
,
1990
, “
Automatic Generation of Forward and Inverse Kinematics for a Reconfigurable Modular Manipulator System
,”
J. Robotic Systems
, Vol.
7
, No.
4
, pp.
599
619
.
12.
Kokkinis
T.
, and
Millies
P.
,
1991
, “
A Parallel Robot-Arm Regional Structure with Actuational Redundancy
,”
Mech. Mach. Theory
, Vol.
26
, No.
6
, pp.
629
641
.
13.
Kumar
V.
,
1992
, “
Instantaneous Kinematics of Parallel-Chain Robotic Mechanisms
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
114
, pp.
349
358
.
14.
Legnani, G., and Riva, R., 1987, “Kinematics of Modular Robots,” Proc. The 7th World Congress on Theory of Mach. and Mech., Sevilla (Spain), pp. 1159–1162.
15.
Lipkin
H.
, and
Duffy
J.
,
1985
, “
The Elliptic Polarity of Screws
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
, Vol.
107
, pp.
377
387
.
16.
Roth, B., 1984, “Screws, Motors, and Wrenches That Cannot Be Bought in a Hardware Store,” Proc. The First Int. Symp. on Robotics Research, Brady, M., and Paul, R., eds., The MIT Press, pp. 679–693.
17.
Shahinpoor
M.
,
1992
, “
Kinematics of a Parallel-Serial (Hybrid) Manipulator
,”
J. of Robotic Systems
, Vol.
9
, No.
1
, pp.
17
36
.
18.
Sklar
M.
, and
Tesar
D.
,
1988
, “
Dynamic Analysis of Hybrid Serial Manipulator Systems Containing Parallel Modules
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
, Vol.
110
, pp.
109
115
.
19.
Sugimoto
K.
, and
Duffy
J.
,
1982
, “
Application of Linear Algebra to Screw Systems
,”
Mech. Mach. Theory
, Vol.
17
, No.
1
, pp.
73
83
.
20.
Waldron
K. J.
,
Raghavan
M.
, and
Roth
B.
,
1989
, “
Kinematics of a Hybrid Series-Parallel Manipulation System
,”
ASME Journal of Dynamic Systems, Measurement, and Control
, Vol.
111
, No.
2
, pp.
211
221
.
21.
Xu, Y. X., Kohli, D., and Weng, T. C., 1992, “Direct Differential Kinematics of Hybrid-Chain Manipulators Including Singularity and Stability Analyses,” Proc. ASME 22nd Biennial Mechanisms Conf., DE-Vol. 45, pp. 65–73.
22.
Veblen, O., and Young, J. W., 1938, Projective Geometry, Vol. I, Blaisdell Publishing Co., New York.
23.
Zanganeh, K. E., and Angeles, J., 1994, “Instantaneous Kinematics and Design of a Novel Redundant Parallel Manipulator,” Proc. IEEE Int. Conf. on Robotics and Automation, Vol. 4, pp. 3043–3048.
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