The simple expressions of equations for force and dynamic analysis of parallel mechanisms can be obtained by expressing the twists and wrenches in a connecting chain by the coordinate vectors on the dual bases of its dual spaces, which are the motion space and the wrench space. The basis of the motion space of a connecting chain is composed of the joint axes in it and the basis of the wrench space is determined to be its dual basis. Expressing the wrenches acting on its links by coordinate vectors on the dual basis gives the closed form concise expressions for the analysis. The relations between active joint torques and wrenches acting on links can be expressed by only matrices composed of dual bases of the connecting chains, and torques of the joints of the tree type mechanism obtained by cutting loops of a parallel mechanism.