In this paper we present a framework for digital human modelling using discrete mechanics and optimal control. Discrete mechanics is particularly well suited for modelling the dynamics of constrained mechanical systems, which is almost always the case when considering complex human models interacting with the environment. We demonstrate that, by using recently developed recursive dynamics algorithms, it is possible to efficiently use discrete mechanics in direct optimal control methods to plan for complex motions. Besides a proper mechanical model, an appropriate objective function is paramount to achieve realistic motions as a solution to an optimal control problem. Hence, several different objective functions, such as for example minimum time or minimum applied torque over the joints, are compared, and the resulting motions are analyzed and evaluated. To further improve the model, we include basic muscular models for the muscles of the shoulder, arm and wrist, and examine how this affects the motions.