Task Driven Geometric Synthesis of Planar and Spherical Mechanisms

This dissertation deals with the classical problem of designing planar and spherical mechanisms for motion generation from a new, task driven perspective. The field of mechanism synthesis dates back to the days of Industrial Revolution and the traditional approach to the problem involves two major steps: type synthesis and dimensional synthesis, where the former deals with the selection of the joint types as well as the topology of a mechanism, and the latter aims at finding the link dimensions of the mechanism. The problem of dimensional synthesis lends itself naturally to mathematical treatment and thus became a highly developed field. This is not, however, quite the case for type synthesis. This is especially disappointing as type synthesis contains the genesis of innovation and as such it plays a key role in mechanism design.;This dissertation presents a new, task driven paradigm for simultaneous type and dimensional synthesis by developing general design equations that integrate the parameters for link dimensions as well as joint types. In particular, for planar mechanism synthesis, a unified representation is developed for planar dyads consisting of all combinations of revolute and prismatic joints. This leads to a novel algorithm for planar four-bar linkage synthesis that not only greatly reduces the complexity in solving the design equations but also allows for the extraction of joint types directly from the given task. Furthermore, the same algorithm is applicable to both the exact synthesis involving five or less given positions as well as approximate synthesis involving six or more positions. The algorithm has also be used to develop a unified algorithm for task driven, simultaneous type and dimensional synthesis of planar six-bar linkages for five position exact synthesis. Central to this new formulation of planar mechanism synthesis is the use of planar kinematic mapping that transforms the problem of linkage synthesis into that of fitting the position data into a pencil of general quadrics associated with planar dyads. The specific joint type of a dyad is identified after the data fitting process. Due to similarity of planar and spherical kinematic mappings, the task driven paradigm has been extended to the synthesis of spherical linkages as well.