Abstract: A new set of equations of rotation matrices and angular velocity vectors of rigid bodies have been proved in this paper.We have presented and discussed a method of kinematic analysis for robots by using the derivative matrices of their rotation matrices,which is based on the set of proved equations,The use of the method in the paper shows that it can replace the conventional,too complex method of diagram of recurrence as a concise one of kinematic analysis for robots,As a result of using the method,we have given a concise close form of expressing of Jacobian matrix for a general robot that conslsts of n links and has n degrees of positional freedom,which is of certain value,The presented method here can be generally regarded as a supplement of the theory of kinematic analysis for rigid bodies.