A C-tree decomposition algorithm for 2D and 3D geometric constraint solving
Computer-Aided Design
Kinematics of line-plane subassemblies in Stewart platforms
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Planar generalized stewart platforms and their direct kinematics
ADG'04 Proceedings of the 5th international conference on Automated Deduction in Geometry
Body-and-cad geometric constraint systems
Computational Geometry: Theory and Applications
Classification of direct kinematics to planar generalized Stewart platforms
Computational Geometry: Theory and Applications
Robotics and Autonomous Systems
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In this paper, we introduce the generalized Stewart-Gough platform (GSP) consisting of two rigid bodies connected with six distance and/or angular constraints between six pairs of points, lines, and/or planes in the base and the moving platform, respectively. We prove that there exist 3850 possible forms of GSPs. We give the upper bounds for the number of solutions of the direct kinematics for all the GSPs. We also obtain closed-form solutions and the best upper bounds of real solutions of the direct kinematics for a class of 1120 GSPs.