Direct kinematics of a 3-PRPS type parallel manipulator
AbstractParallel manipulators with six degrees of freedom and three limbs have a large workspace and less complex singular configurations compared to the parallel manipulators with six degrees of freedom and six limbs. This paper is presented to solve the direct kinematics of a novel 3-PRPS type parallel manipulator with six-degrees-of-freedom, where P, R, and S are prismatic, revolute and spherical kinematic pairs respectively. The considered parallel manipulator is formed by connecting a moving platform with a fixed platform (base) through three closing kinematic chains of a PRPS type in which the prismatic kinematic pairs are active and they are located on a fixed platform and legs. The constant and variable parameters of the considered parallel manipulator characterizing its geometry and kinematics respectively are determined. In the direct kinematics, the positions of the moving platform are determined by the known constant parameters of the links and the given variable parameters of the active kinematic pairs. An analysis of the obtained equations of the direct kinematics showed that the variable parameters of the active prismatic kinematic pairs are set free, and these equations are reduced to a 16th –order polynomial equation with passive kinematic pairs variables. Numerical examples of the considered parallel manipulator’s direct kinematics are presented, and the results showed that the direct kinematics equations have four solutions corresponding to the four assemblies of the parallel manipulator.
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