Direct drive robots are widely used to perform high precision positioning, and advanced control algorithms are applied to attain the desired performance. Small direct drive manipulators are widely used in aerospace, biotechnology, instrumentation, medicine, micro manufacturing, high-density integrated circuits and VLSI fabrication, etc. This paper studies non-linear modelling, analysis and control of direct drive robots to guarantee the desired level of performance. We are particularly interested in the physical laws to model mechanical-electromagnetic phenomena and effects, and the integration of electric motors is a key factor to design high performance direct drive robots. The non-linear mathematical model, found using the Lagrange equations of motion, is applied in non-linear analysis and design. The design method is described and validated. The design concept uses the Hamilton-Jacobi and Lyapunov theories to synthesize robust tracking controllers. It is illustrated that minimizing a non-quadratic performance functional, a bounded control law is analytically designed using necessary conditions for optimality. The sufficient conditions for robust stability are examined using the criteria imposed on positive-definite return functions. Results indicate that the reported method allows one to guarantee robust accurate tracking and disturbance attenuation. A two-degree-of-freedom prototype of direct drive manipulator is described, and the achieved performance is documented and discussed.