本文首先利用 spatial notation 理论建立了刚体的达朗伯原理、高斯原理和高斯最小拘束原理.然后,将其用于机器人端杆加速度受约束时的动力学分析和建模,并利用动态规划方法求解机器人的正动力学问题,得到了计算关节加速度的线性递推公式.用简单而统一的办法来处理附加于机器人系统的约束条件,特别适合于分析空间、水下和冗余机器人的复杂运动. In this paper, we firstly use the theory of spatial notation to establish the principle of Darumber, the principle of Gauss and the Gaussian minimum constraint, and then use it to solve the dynamics analysis and modeling when the robot end-rod acceleration is constrained. The robot’s positive dynamics problem is solved by a linear recursion formula for calculating the joint acceleration.The simple and uniform method to deal with the constraints attached to the robot system is especially suitable for the analysis of the complex movement of space, underwater and redundant robots.