Human-robot coordination system is one feasible solution for a robot to assist human to conduct tasks. The most important specification is safety, especially for the system with physical interaction. To solve this problem, we developed a passive dance robot to perform ballroom dances in cooperation with a human. The paper aims to study the human-robot coordination via a passive dance robot installed with servo brakes rather than servo motors usually in active robot. The motion of passive robot is usually driven by human force. To this end, the dynamic manipulability was utilized to optimize the structure design and analyze the acceleration capability, leading to reduced human burden. Further, the non-time based path tracking algorithm was proposed. To realize non-time based control, a fast orthogonal projection algorithm was proposed. Experiments were carried out to verify the proposed methods in this paper.