This paper presents a new method for generating motion profiles of rotating bodies, for example, the joint angle motion of mechanical systems such as space manipulators and antennas. In the planning of a motion from the given initial conditions to the final conditions, there are many constraints that should be considered, for example, actuator torque limits, rate limits, jerk limits, etc. Furthermore, flexibility of a system cannot be ignored in general. Vibration suppression is of great importance in some applications. For stationary boundary conditions (rest-to-rest cases), if the only constraint is the torque limit, a simple bang-bang type profile is the optimal one. However, if we consider more general boundary conditions, complex constraints, and vibration suppression conditions, the problem becomes considerably complicated. In this study, motion planning for a fixed motion time is considered. The control input or the acceleration of the motion is expressed as a linear superposition of triangle waves whose weight coefficients are determined in order to optimize the motion profile. In this formulation, all the boundary conditions and several constraints, including vibration suppression conditions, are expressed as linear equality and inequality constraints. Therefore, by appropriately setting the performance index, the problem becomes a linear programming problem and can be solved efficiently.