Abstract: Based on the spatial notation theory,D Alembert's principle,Gauss principle and Gaussian principle ofleast constraint for rigid body are discussed.These principles are applied to the dynamic analysis and modelling of the robot while the accelerations of the manipulator are constrainted.In solving the positive dynamics problem of robot,dynamic planning method is also used.As a result,linear recursion formulae ofcomputing the joint accelerations are obtained.The algorithm is simple and general,can be used conveniently in analyzing the complicate,motions for spatial,underwater and redundant robots.