Interactive Dimensional Synthesis of Spherical 6R Closed Chains and Planar Parallel Manipulator via Constraint Manifold Modification

Abstract

In this thesis the dimensional synthesis of a spherical 6R closed chain and a class of planar parallel manipulator is discussed. The kinematic constraints of the planar as well as the spherical mechanisms relate to the constraints that limit the position of the links of planar and spherical closed chains in the Cartesian space. Quaternions are used to represent planar and spherical displacements. The problem of synthesizing smooth piecewise rational motions is converted into that of designing smooth piecewise rational curves in the space of quaternions(image space). The kinematic constraints are transformed into geometric constraints for the design of quaternion image curves. An interactive, user friendly graphical tool is used for dimensional synthesis. The graphical tool allows the user to visually contain the image curve by simple geometric manipulation of the size, orientation, and the location of the constraint surfaces that is developed. The process is intuitive and lends designers an understanding of the mechanism design methodology.