Coordinating multiple manipulators in a shared workspace while considering their dynamics is an important problem. This problem of collision-free coordination arises in assembly, materials transfer, and welding workcells. Previous approaches that considered robot dynamics have typically been restricted to coordinating just two or three manipulators, even when their paths are specified. We address the task of coordinating the motions of multiple manipulators when either their trajectories or their paths are given. By exploiting a fundamental time scaling law for manipulators based on their dynamics, we identify sufficient conditions for collision-free coordination of the robots when the velocity profiles can be uniformly time-scaled and the robot start times can be varied. We describe an approach that develops mixed integer programming formulations of these problems, where the time scaling factors are linear variables, to automatically minimize completion time. This method can potentially coordinate the motions of many manipulators.