Design Criteria for Serial Chains Based on Kinetic Energy Partition Values

Abstract

In this article, a description of the kinetic energy partition values (or energy ratios) of serial chain mechanisms, as well as their rates of change, are presented. These energy ratios are indicators of the kinetic energy distribution within the system and they exploit the structure of the effective inertia matrix. The rates of change of the kinetic energy partition values with respect to the input parameters of the system indicate the sensitivity of change of the kinetic energy, meaning that a high value for the partition value rate of change together with a high operational state implies that the amount of kinetic energy flowing in the system is large further implying a loss of precision in the system due to large inertial torques applied about the joint axes. Two design criteria, one based on the kinetic energy partition values and another based on their rates of change, are presented. A two degree-of-freedom (DOF) mechanism is used to illustrate the solution of a multi-criteria design optimization problem where three design criteria are considered: a kinetic energy partition value criterion, a force capability criterion and an effective mass criterion. The design variables for the optimization problem are the transmission reduction ratios of the actuators. It is shown that the reduction ratios significantly influence the kinetic energy distribution within the system due to the high levels of kinetic energy in the rotary mass of the prime movers.