Ph.D., Colorado State University, December 2014
Major Professor: Anthony A. Maciejewski
It is common practice to design a robotís kinematics from the desired properties that are locally specified by a manipulator Jacobian. Conversely, one can determine a manipulator that possesses certain desirable kinematic properties by specifying the required Jacobian. For the case of optimality with respect to fault tolerance, one common definition is that the post-failure Jacobian possesses the largest possible minimum singular value over all possible locked-joint failures. This work considers Jacobians that have been designed to be optimally fault tolerant for 3R and 4R planar manipulators. It also considers 4R spatial positioning manipulators and 7R spatial manipulators. It has been shown in each case that multiple different physical robot kinematic designs can be obtained from (essentially) a single Jacobian that has desirable fault tolerant properties. In the first part of this dissertation, two planar examples, one that is optimal to a single joint failure and the second that is optimal to two joint failures, are analyzed. A mathematical analysis that describes the number of possible planar robot designs for optimally fault-tolerant Jacobians is presented. In the second part, the large family of physical spatial positioning manipulators that can achieve an optimally failure tolerant configuration are parameterized and categorized. The different categories of manipulator designs are then evaluated in terms of their global kinematic properties, with an emphasis on failure tolerance. Several manipulators with a range of desirable kinematic properties are presented and analyzed. In the third part, 7R manipulators that are optimized for fault tolerance for fully general spatial motion are discussed. Two approaches are presented for identifying a physically feasible 7R optimally fault tolerant Jacobian. A technique for calculating both reachable and fault tolerant six-dimensional workspace volumes is presented. Different manipulators are analyzed and compared. In both the planar and spatial cases, the analyses show that there are large variabilities in the global kinematic properties of these designs, despitebeing generated from the same Jacobian. One can select from these designs to optimize additional application-specific performance criteria.