This paper presents a recursive dynamic formulation for modeling and simulation of spatial mechanisms with elastic beams. In order to circumvent some difficulties in the convential assumed mode approach, each flexible link is modeled with finite elements. The motion of the flexible link comprises the rigid body motion and elastic deformation. The elastic deformations are represented by nodal coordinates relative to the moving coordinate system fixed to the link. Recursive kinematic relationships are derived between finite beam elements. Using variational equations of motion for the one beam element and recursive relationships, the equations of motion for the open-chain flexible bodies are derived in terms of relative joint and nodal coordinates. For closed-loop systems, Lagrange multipliers are used to generate the equations of motion with kinematic constraints. The proposed method models geometric nonlinear effects and axial tensioning effects automatically. Also, the difficulties of the mode selection in the assumed mode approach is avoided. Numerical examples illustrate the effectiveness of this approach.

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