| Citation: | HUANG Xiguang, HUANG Xu. Direct kinematics of a spatial parallel mechanism based on conformal geometric algebra[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(12): 2377-2381. doi: 10.13700/j.bh.1001-5965.2016.0917(in Chinese)
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An algorithm is proposed for the direct kinematics analysis of a spatial general 3-RPS parallel mechanism based on conformal geometric algebra (CGA). The angle between the axis of an arbitrary kinematic chain and the plane of the fixed platform can be regarded as the unknown variable. The mathematical expression of the position of the spherical joint connecting the moving platform with the kinematic chain can be expressed in the unknown variable based on CGA. The outer product of two space balls and a flat surface are constructed two times, and the corresponding points of the remaining two vertices of the moving platform are obtained respectively. The 16th degree input-output polynomial equation in the unknown variable is straightforwardly obtained by distance formula and all 16 sets of closed-form solutions can be achieved. The algorithm avoids the use of rational angles or matrices, and complex computations for nonlinear and multivariable equations. A numerical example is given to demonstrate geometric characteristics of the motion and the algorithm is intuitive.
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