Development of a novel method of modeling large deformation planar flexible mechanisms connected with mass blocks or rigid bodies based on ANCF

Based on the Absolute Node Coordinate Formulation (ANCF), An efficient and simple method to treat mass blocks or rigid bodies in large deformation planar flexible mechanisms is proposed, namely the equivalent beam (EB) method, and the corresponding equivalent equations are provided based on rigid body plane motion. Through this method, the rigid body connected to the flexible body is equivalent to a flexible beam with higher stiffness, and a unified ANCF is used to establish the model of the EB. In the modeling process, only the node constraints of EBs and flexible bodies are considered, greatly simplifying the constraint analysis and improving modeling efficiency. Moreover, the influence of the inertia force and gravity in the gravitational field of rigid bodies on the system are fully considered by the method, effectively improving the accuracy. Meanwhile, six constraint forms based on one-dimensional two-node beam element are summarized, and corresponding node coordinate expressions are provided. Finally, the static and dynamic analyses on three typical planar flexible mechanisms containing large deformation beams are conducted by the method, and the results are compared with those obtained by the lumped mass (LM) method and finite element analysis (FEA), fully verifying the superiority of the EB method.