5. Spatial Parallel Robotic Machines with Prismatic Actuators

In this chapter, we first introduce a fully six degrees of freedom fully-parallel robotic machine with prismatic actuators. Then several new types of parallel mechanisms with prismatic actuators whose degree of freedom is dependent on a constraining passive leg connecting the base and the platform is analyzed. The mechanisms are a series of n-dof parallel mechanisms which consist of n identical actuated legs with six degrees of freedom and one passive leg with n degrees of freedom connecting the platform and the base. This series of mechanisms has the characteristics of reproduction since they have identical actuated legs, thus, the entire mechanism essentially consists of repeated parts, offering price benefits for manufacturing, assembling, and maintenance.

A simple method for the stiffness analysis of spatial parallel mechanisms is presented using a lumped parameter model. Although it is essentially general, the method is specifically applied to spatial parallel mechanisms. A general kinematic model is established for the analysis of the structural rigidity and accuracy of this family of mechanisms. One can improve the rigidity of this type of mechanism through optimization of the link rigidities and geometric dimensions to reach the maximized global stiffness and precision. In what follows, the geometric model of this class of mechanisms is first introduced. The virtual joint concepts are employed to account for the compliance of the links. A general kinematic model of the family of parallel mechanisms is then established and analyzed using the lumped-parameter model. Equations allowing the computation of the equivalent joint stiffnesses are developed. Additionally, the inverse kinematics and velocity equations are given for both rigid-link and flexible-link mechanisms. Finally, examples for 3-dof, 4-dof, 5-dof, and 6-dof are given in detail to illustrate the results.