Nonlinear Dynamic Modelling of a Revolute-Prismatic Flexible Composite-Material Robot Arm

In this work, a nonlinear dynamic model is derived to study the motion of a planar robot arm consisting of one revolute and one prismatic joint. Both links of the arm are considered to be flexible and are assumed to be constructed from either isotropic conventional metallic materials or anisotropic laminated fibrous composite materials. The model is derived based on the Timoshenko beam theory in order to account for the rotary inertia and shear deformation. In addition, a nonlinear strain-displacement field is implemented to consider the large deformation of the arm. The deflections of the links are discretized by using a shear-deformable beam finite element. The governing equations of motion are derived from Hamilton’s principle. The digital simulation studies examine the combined effects of geometric nonlinearity, rotary inertia, and shear deformation on the arm’s end effector displacements. Furthermore, effects of the fiber’s angle and material orthotropy on the end effector displacements and maximum normal bending stress are studied.