| This dissertation focuses on the kinematic synthesis of mechanical linkages in order to guide an end-effortor so that it maintains contact with specified objects in its workspace. Assuming the serial chain does not have full mobility in its workspace, the contact geometry is used to determine the dimensions of the serial chain. The approach to this problem, is to use the relative curvature of the contact of the end-effector with one or more objects to define velocity and acceleration specifications for its movement. This provides kinematic constraints that are used to synthesize the dimensions of the serial chain. The mathematical formulation of the geometric design problem, leads to systems of multivariable polynomial equations, which are solved exactly using sparse matrix resultants and polynomial homotopy methods.;The results from this research yield planar RR and 4R linkages that match a specified contact geometry, spatial TS, parallel RRS and perpendicular RRS linkages that have a required acceleration specification. A new strategy for a robot recovery from actuator failures is demonstrated for the Mars Exploratory Rover Arm. In extending this work to spatial serial chains, a new method based on sparse matrix resultants was developed, which solves exact synthesis problems with acceleration constraints. Further the research builds on the theoretical concepts of contact relationships for spatial movement.;The connection between kinematic synthesis and contact problems and its extension to spatial synthesis are developed in this dissertation for the first time and are new contributions. The results, which rely upon the use of surface curvature effects to reduce the number of fixtures needed to immobilize an object, find applications in robot grasping and part-fixturing.;The recovery strategy, presented in this research is also a new concept. The recognition that it is possible to reconfigure a crippled robotic system to achieve mission critical tasks can guide the development of robust task planning algorithms and influence future robot design. |
