Elastodynamic modeling and analysis of a 4SRRR overconstrained parallel robot

Abstract. To address the unstructured on-site work requirements in shipyards and large-steel-structure manufacturing plants, this paper develops a 4SRRR (where S is spherical and R is rotational) quadruped wall-climbing robot, establishes a dynamic analytical model, and analyzes its natural frequencies. First, Timoshenko beam elements, which consider shear deformation, are used to replace Euler–Bernoulli beam elements, and the dynamic control equations for each element are established. The Lagrangian equation is then used to derive the dynamic control equations for the rods. Second, based on the theory of multipoint constraint elements and linear algebra, a set of independent displacement coordinates is established for the connection points between rods and the moving platform, rods and rods, and rods and the fixed platform. The global independent generalized displacement coordinates of the mechanism are obtained by combining these independent displacement coordinates with the internal node displacement coordinates. Third, the overall dynamic control equations of the mechanism are obtained by combining the Lagrangian equation with the global independent generalized displacement coordinates. Comparing the results with the finite element method (FEM) established using Ansys software, it is found that even when the rods are considered single elements the error in the first three natural frequencies does not exceed 3.5 %. When the rods are divided into three elements, the error in the first six natural frequencies does not exceed 5 %. Further increasing the number of rod divisions results in diminishing reductions in the error.