Kinematic analysis of a new 3-PRRS tripod type parallel manipulator

Abstract

The closed kinematic chain increases the strength of the parallel manipulator (PM) and reduces the loads applied to the drive links. High carrying capacity and good dynamic performance allow the use of such systems in many industries. Currently, in practice, mainly PM with six degrees of freedom and six legs (hexapods), based on the Stewart platform, are used. Since the moving platform of such PM is driven by six legs, its workspace will be small. An increase in the workspace of a parallel robot can be obtained by reducing the number of legs connecting the moving platform to the base. PM with three legs (tripods) usually has three degrees of freedom, and, they cannot fully provide a given movement of a moving platform with six degrees of freedom. The paper presents a new 3-PRRS type tripod with six degrees of freedom and three legs, each of which consists of PRRS kinematic chains (P - prismatic, R - revolute, S - spherical kinematic pairs). The purpose of the work is to determine the workspace and to solve the direct and inverse problem of speed of the tripod. It is known that revolute kinematic pairs restrict the movement to the legs of this tripod, therefore, the workspace was determined taking into account the relationship between the parameters that determine the position X_P,Y_P,Z_P and orientation ψ,θ,ϕ of the moving platform center in space. The Jacobi matrixes were derived from the equations of the closed loops, the direct and inverse velocity problems of kinematics are solved by adding the constraints equations of revolute kinematic pairs to the matrix. Thus, in the new PM 3-PRRS type tripod with six degrees of freedom, the number of legs was reduced from six to three compared to the Stewart platform, and the workspace was increased by replacing the prismatic kinematic pairs by revolute kinematic pairs.