| Taking two kinds of parallel mechanisms with 3-DOF and 4-DOF respectively as the subjects, this paper analyzed the structural characteristics, degree-of-freedom, kinematical output matrices and criterion of mobility type for these two kinds of mechanisms. Also, some kinematical problems were studied for parallel mechanism. Firstly, Denavit-Hartenberg method was applied to establish the inverse and forward kinematical models of parallel mechanisms, and a closed solution of inverse kinematics was obtained. For 3-DOF parallel mechanism, a complete input-output relationship was determined. Because the forward problem of 4-DOF parallel mechanism is in the form of multi-variables nonlinear equations, One-dimensional Search Method was used to determine a group of solutions, and a fast algorithm was given so that the requirements of real-time control could be met. In the study of the workspace, the ultimate boundary searching method was established based on the solution of the inverse kinematical problem. The workspace's boundary curve was determined for the platform center of the 3-DOF parallel mechanism. The influence of structural parameters upon the workspace of parallel manipulators was also discussed by changing the dimensions of the mechanism. The singularity of the mechanism was analyzed by determining the properties of the Jacobian matrices of the kinematical chain. The shape of workspace for the 4-DOF parallel mechanism was obtained based on the constrained condition. Finally, the kinematical simulation of three transfer parallel robot was realized based on the C++Builder and OpenGL.
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