The coupling relationship among the positional and orientational variables of the moving platform of general 6-SPS parallel mechanisms was studied. Six in nine variables were expressed by the three remainder variables, so the position variables were expressed by orientational variables. Applying Grbner basis algorithm, fifteen four order compatible algebraic equations were obtained, which contained the three remainder variables. The orthogonal complement method was used several times to eliminate the redundant variables, by this way the problem of the forward kinematics analysis of the general 6-SPS parallel mechanisms can be simplified as several twenty order algebraic equations in the end. It is verified that these equations have the same solutions.
Merlet J P. Parallel Robots[M]. Berlin: Springer, 2006.
[3]
Hunt K H, Primrose E J F. Assembly Configurations of Some In- parallel- actuated Manipulators [J]. Mechanism and Machine Theory, 1993,28(1): 31-42.
[4]
Wampler C W. Forward Displacement Analysis of General Six-in-parallel SPS Platform Manipulators Using Soma Coordinates[J]. Mechanism and Machine Theory, 1996,31 (3) : 331-337.
[5]
Husty M L. An Algorithm for Solving the Direct Kinematics of General Stewart - Gough Platforms [J]. Mechanism and Machine Theory, 1996,31(4) : 365-379.
[6]
Raghavan M. The Stewart Platform of General Geometry Has 40 Configurations[J]. ASME Journal of Mechanical Design, 1993,115 (2) : 277-282.
[7]
Zhang Chang- de, Song Shin- Min. Forward Position Analysis of Nearly General Stewart Platforms [J]. ASME Journal of Mechanical Design, 1994, 116(1) :54-60.
[8]
Wu Wenda, Huang Yuzheng. The Direct Kinematic Solution of the Planar Stewart Platform with Coplanat Ground Points [J]. Journal of Computational Mathematics, 1996,14(3) :263-272.
[9]
Dhingra A K, Almadi A N, Kohli D. A Grobner- Sylvester Hybrid Method for Closed- form Displacement Analysis of Mechanisms [J]. ASME Journal of Mechanical Design, 2002, 122 (4) : 431- 438.