Dynamical decoupled design of a two-dof planar differential belt driven robot using multibody system dynamics

Abstract

In this paper, a novel dynamical decoupled design of a two-dof differential belt-driven parallel robot is proposed. Equation of motion of the robot, including the inside mechanical properties of pulleys and sliders, are derived by the symbolic multibody dynamics system (MBD) analysis. First, the constraint of a mobile idle pulley and belt are derived, which has not been dealt with in previous studies of general symbolic MBD. A method for overcoming the over-constraints of the closed belt is proposed. The symbolic MBD model of the robot by the differential algebraic equation is established using Mathematica, thus deriving the kinematics and forward dynamics equation of the robot in a symbolic manner. Next, as an upstream mechanism design of the differential belt drive robot, that the off-diagonal terms of the generalized inertial matrix and the generalized viscous matrix of the equation of motion are set to zero by giving additional inertia, and additional viscosity is derived, that enable a dynamic non-interference design for the differential belt drive robot. Using Simscape Multibody, which is one of the general-purpose Numerical MBD software, an extended package of MATLAB/Simulink, a numerical model with mechanical parameter values such as mass, the moment of inertia, and viscosity coefficient assuming an actual mechanism is constructed. The feasibility of the quantity of the added mass and the added viscosity is discussed using a mechanical model assuming an actual machine. The effectiveness of the proposed decoupled design were confirmed by numerical simulations using Simscape Multibody.