We describe new architectures for the efficient computation of redundant manipulator kinematics (direct and inverse). By calculating the core of the problem in hardware, we can make full use of the redundancy by implementing more complex self-motion algorithms. A key component of our architecture is the calculation in VLSI hardware of the Singular Value Decomposition of the manipulator Jacobian. Recent advances in VLSI have allowed the mapping of complex algorithms to hardware using systolic arrays with advanced computer arithmetic algorithms. We use CORDIC arithmetic in the novel design of our special-purpose VLSI array, which is used in computation of the Direct Kinematics Solution (DKS), the manipulator Jacobian, as well as the Jacobian Pseudoinverse. Application-specific (subtask-dependent) portions of the inverse kinematics are handled in parallel by a DSP processor which interfaces with the custom hardware and the host machine. The architecture and algorithm development is valid for general redundant manipulators and a wide range of processors currently available and under development commercially.