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Dynamic simulation requires the computationally expensive calculation of joint accelerations, while in kinematic simulation these accelerations are known based on a given trajectory. This paper describes a hybrid kinematic and dynamic simulation method that can be applied to the simulation of running machines to speed up the computations over that of a dynamic simulation. This is possible because much of the time the legs of a running machine are in the air and their trajectories are directly specified and tightly controlled. The method is more flexible than dynamic simulation alone because it allows joints to be either motion-controlled or force-controlled. It is general to all robotic systems with tree structures, and fully motion-controlled or force-controlled kinematic loops. It should work best for machines with appendages that are motion-controlled, such as those encountered in underwater and space manipulation.