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A geometrically accurate deformable-body approach for the analysis of robotic and parallel-mechanism systems

Abstract Strength and durability investigations of parallel-mechanism (PM) and robotic systems, used as integral part in modern manufacturing, are necessary at the virtual design stage. Nonetheless, because of the limitations of existing finite element (FE) approaches, flexible-link geometries are often simplified or distorted when converting solid models to FE analysis meshes. This article introduces and demonstrates the use of a new unified geometry/analysis approach for the small-deformation analysis of robotic and parallel mechanism (RPM) systems with flexible links. The approach used in this investigation integrates the geometrically accurate absolute nodal coordinates formulation (ANCF) with the computationally efficient floating frame of reference (FFR) formulation that allows for systematic elimination of high-frequency and insignificant deformation modes. The proposed ANCF/FFR approach allows modeling accurately the stress-free reference configuration geometry, captures the dynamic coupling between the rigid-body and elastic displacements, is based on a unified geometry/analysis mesh that eliminates the need for geometry/analysis model conversion or coordinate transformation, and allows for efficient and accurate solution of the nonlinear dynamic equations that govern the RPM motion. The formulation of the spatial ANCF/FFR equations of motion including the elastic (stress) forces using a general continuum-mechanics approach is presented, and use of the strain split method (SSM) as an FE locking-alleviation technique is discussed. A frequency-convergence analysis of flexible links with tapered geometry is performed and the obtained numerical results are compared with solutions obtained using commercial FE software. The application of the new procedure in the nonlinear dynamics simulations of RPM systems is demonstrated using a spatial parallel mechanism that includes flexible links and prismatic, revolute, and spherical joints.