Dynamic analysis and synthesis of geared robotic mechanisms

The objective of this research is to develop a systematic approach for the dynamic analysis of geared robotic mechanisms and to establish systematic and rational methodologies for the determination of gearing configuration and gear ratios.; First, systematic methodologies are developed for the formulation of equations of motion and reaction forces analysis of geared robotic mechanisms. The formulation of dynamic equations is based on the concepts of equivalent open-loop chain and canonic graph representation of such a mechanism. It is shown that the generalized inertia forces can be formulated by separating the contribution due to motion of major links and that due to the relative motion of carried links with respect to major links. Then, generalized active forces are formulated and combined with generalized inertia forces to form the equations of motion. It is also shown that reaction force analysis of such mechanisms can be efficiently carried out by a link-by-link forward evaluation of carried links along its transmission lines followed by a link-by-link backward evaluation of major links along the equivalent open-loop chain.; Then, two methodologies are developed for the determination of gearing configuration and gear ratios. The first methodology considers the design from both kinematics and dynamics points of view. It is shown that, through proper choice of gear ratios, certain gear-coupled manipulators can be designed to possess kinematic isotropy and maximum acceleration capacity (KIMAC) conditions at a given reference point while individual-joint drive manipulators can not be designed to possess such conditions. The train values of those gear-coupled manipulators can be thought of as a product of two-stage gear reductions. The second-stage gear reduction is used to define the kinematic isotropic condition while the first-stage gear reduction is used to optimize the acceleration capacity. The second methodology considers the design from just the dynamics point of view. It is shown that, to achieve a maximum acceleration capacity (MAC), the mass inertia matrix of the input links reflected at the joint-space should be equal to that of the major links. It is also shown that the maximum acceleration capacity is independent of the gearing configuration.; The methodologies developed in this research provide an efficient and systematic approach for dynamic analysis and synthesis of a general class of geared robotic mechanisms.