Analytical and simulation modeling of flexible joints for mechatronic and robotic systems

To operate in unstructured environments, robots must have the property of passivity which can be realized either through control algorithms or physical elastic elements. Flexible elements can be used to recover energy, absorb peak shock loads, and simplify the control system, generally reducing the requirements for accurate information about the robot's environment. The modeling of flexible bodies, for example using the finite element method, is computationally demanding, which limits the simulation of the dynamic behavior of robots with flexible elements. In this paper, we propose an approach for analytical and simulation modeling of flexible joints using the planar case of a spatial spring model, which provides high speed simulation without loss of accuracy. The synthesis of the flexible joint model consists of numerical optimization of the nonlinear stiffness diagrams of the rotational and translational degrees of freedom for the planar case of the spatial spring model. The synthesized flexible joint model allows describing the relative motion of two links. In the first step of the synthesis, the flexible joint is optimized by finite element method to find the reference data of applied load and corresponding deformations. In the second stage, an optimization problem is solved to find nonlinear stiffness diagrams for the planar case of the spatial spring model; the criterion is to minimize the error between the reference data and the optimized spring model. In the third stage, the obtained results are verified by simulation and/or physical experiment. The method of analytical and simulation modeling of flexible joints with the help of spatial spring model is proposed, the procedure of optimization of stiffness of spring model is proposed, verification in simulation environment is carried out, full-scale experiment is carried out, comparison of simulations by finite element method, simulation with the help of spring model and results of full-scale experiment is provided. The proposed method allows the calculation of a simulation model of a flexible joint approximately twice as fast as the finite element method. The proposed model of flexible joint is necessary to increase the speed of simulation modeling of mechatronic and robotic systems with compliant hinges without loss of accuracy. Approbation of the method is planned for the design of locomotion, manipulation, wearable robots, and gripper devices.