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The dynamic analysis of a flexible-link-joint robot colliding with its environments is presented in this paper. Kinematics of both rotary-joint motion and link deformation is described by 4×4 homogenous transformation matrices. Both the stretching deformation, bending deformation and the torsional deformation of the flexible links are considered. Furthermore, the flexibility and the mass of the joint are considered too. The concept of impact force potential energy is introduced, so that the generalized forces due to the impact force can be computed easily. The Lagrange dynamic equations are used to establish the complete mathematic model of the system with impact. Dynamics simulation of a spatial flexible-link-joint manipulator arm is given as an example to validate the algorithm presented in this paper. And the numerical results indicate that the flexibility of the link and joint have distinguished influence on the impact dynamics of the flexible robots.

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