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In this research, two important concepts concerning parallel robots are investigated: compliance and fault tolerance. First, we address the issue of synthesizing a suitable compliance. This is an important problem since a well-designed compliance/stiffness mechanism can provide proper force regulation and compensate for the inevitable inaccuracy of traditional control systems. Mathematically, the compliance/stiffness of a robotic mechanism is usually modeled by a 6 by 6 symmetric positive definite matrix at an equilibrium point using screw theory. Synthesis of unloaded spatial stiffness problems has attracted some attention recently and several techniques have been developed to systemically synthesize compliance mechanisms with a given symmetric positive definite spatial stiffness matrix. However, when an external wrench is exerted on the mechanism and the mechanism moves away from its unloaded equilibrium, the modeled compliance/stiffness matrix becomes non-symmetric. In this study, the non-symmetric stiffness matrix for a robotic mechanism is derived and converted into a particularly simple form using matrix algebra. Based on the canonical form of the stiffness matrix, two novel procedures are presented for the first time for synthesizing a desired non-symmetric stiffness matrix for a planar structure when there is an external load that puts the system in a loaded equilibrium. The second part of the dissertation focuses on the problem of designing nominal manipulator Jacobians that are optimally fault tolerant to one or more joint failures. In this work, optimality is defined in terms of the worst case relative manipulability index. While this approach is applicable to both serial and parallel mechanisms, it is especially applicable to parallel mechanisms with a limited workspace. It is shown that a previously derived inequality for the worst case relative manipulability index is generally not achieved for fully spatial manipulators and that the concept of optimal fault tolerance to multiple failures is more subtle than previously indicated. The final goal of this work is to identify the class of eight degree-of-freedom Gough-Stewart platforms that are optimally fault tolerant to up to two locked joint failures. Configurations of serial and parallel robots that achieve optimal fault tolerance for a give Jacobian are presented as results of this study.