The paper presents the position analysis of a spatial structure composed of two platforms mutually connected by one RRP and three SS serial kinematic chains, where R, P, and S stand for revolute, prismatic, and spherical kinematic pair, respectively. A set of three compatibility equations is laid down that, following algebraic elimination, results in a 28th-order univariate algebraic equation, which in turn provides the addressed problem with 28 solutions in the complex domain. Among the applications of the results presented in this paper is the solution to the forward kinematics of the Tricept, a well-known in-parallel-actuated spatial manipulator. Numerical examples show adoption of the proposed method in dealing with two case studies.
Issue Section:
Research Papers
1.
Weck
, M.
, and Staimer
, M.
, 2002, “Parallel Kinematic Machine Tools–Current State and Future Potentials
,” CIRP Ann.
0007-8506, 51
(2
), Feb. pp. 671
–683
.2.
Neumann
, K. E.
, 1988, “Robot
,” US Patent No. 4,732,525, (22 Mar.).3.
Siciliano
, B.
, 1999, “The Tricept Robot: Inverse Kinematics, Manipulability Analysis and Closed-Form Direct Kinematics Algorithm
,” Robotica
0263-5747, 17
, pp. 437
–445
.4.
Merlet
, J.-P.
, 2000, Parallel Robots
, Kluwer
, Dordrecht.5.
Hunt
, K. H.
, 1978, Kinematic Geometry of Mechanisms
, Clarendon
, Oxford.6.
Joshi
, S. A.
, and Tsai
, L. W.
, 2003, “The Kinematics of a Class of 3-DOF 4-Legged Parallel Manipulators
,” ASME J. Mech. Des.
1050-0472, 125
(1
), pp. 52
–60
.7.
Craig
, J. J.
, 1989, Introduction to Robotics: Mechanics and Control
, Addison–Wesley
, Reading, MA.8.
Lin
, W.
, Crane
, C. D.
, and Duffy
, J.
, 1994, “Closed-Form Forward Displacement Analysis of the 4-5 In-Parallel Platforms
,” ASME J. Mech. Des.
1050-0472, 116
(1
), pp. 47
–53
.Copyright © 2006
by American Society of Mechanical Engineers
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