This paper discusses a methodology for fixed-time simulations of optimal movements of a mechanical system, between specified initial and target configurations, without any a priori knowledge on the trajectory between those. It is primarily aimed at human movement simulations with muscular controls. The basic formulation considers both displacements and forces as unknowns during the movement, connects them, and utilizes a finite element time discretization for solving the whole fixed-time interval simultaneously. Through a consistent interpolation of all kinetic and kinematic variables, the formulation becomes general, needing only minimal input for description of a particular problem, but also eliminating errors inherent in many forms of time-integration. The same consistency allows systematic formulations of a large class of optimization cost functions, primarily focussing on the mechanical behavior of the system rather than on the matching of previously measured movements. It thereby allows the use of robust and efficient general optimization algorithms. Kinetic and kinematic constraints can restrict the movement. As an example of the general setting, a simplified human movement is studied, with different choices of controls (joint moments or muscular tensions), and with different optimization criteria. The example shows that the simulation results are strongly dependent on these choices, in particular that smoothness of movement demands forces considerably higher than the strictly minimum ones. A larger example shows that more complex constraints can be handled within the setting proposed, but also the effects from the fixed-time assumption.