Angularity and axiality of a Schönflies parallel manipulator

SUMMARYThis paper presents a systematic approach to compute the angularity and the axiality indices for a Schönflies parallel manipulator. Angularity index may be considered as a measure of the sensitivity of the mobile platform to changes in rotation, while axiality index can be used to measure the sensitivity of the OP of the mobile platform to changes in translation. Since both indices were inspired by very fundamental concepts of classical kinematics (angular velocity vector and helicoidal velocity field), they offer a clear and simple physical meaning, which may be useful to the designer of parallel manipulators. Moreover, both dexterity indices do not require obtaining a dimensionally homogeneous Jacobian matrix, nor do they depend on having similar types of actuators in each manipulator's leg. Detailed numerical examples are given in order to illustrate the computation of the dexterity indices.

Two Natural Dexterity Indices for Parallel Manipulators: Angularity and Axiality

This paper introduces two novel dexterity indices, namely, angularity and axiality, which are used to estimate the motion sensitivity of the mobile platform of a parallel manipulator undergoing a general motion involving translation and rotation. On the one hand, the angularity index can be used to measure the sensitivity of the mobile platform to change in rotation. On the other hand, the axiality index can be used to measure the sensitivity of the operation point (OP) of the mobile platform to change in translation. Since both indices were inspired by very fundamental concepts of classical kinematics (angular velocity vector and helicoidal velocity field), they offer a clear and simple physical insight, which is expected to be meaningful to the designer of parallel manipulators. Moreover, the proposed indices do not require obtaining a dimensionally homogeneous Jacobian matrix, nor do they depend on having similar types of actuators in each manipulator's leg. The details of the methodology are illustrated by considering a classical parallel manipulator.

Multi-Criteria Optimal Design of Parallel Manipulators Based on Natural Frequency

The Stewart manipulator has characteristics of low natural frequency, high cost and large size which make it difficult to obtain optimum performance with high dynamic response. The lowest natural frequency in the total workspace and average of six frequencies at home configuration of Stewart manipulator are introduced as indices to evaluate dynamic stability. Multi-criteria optimal design based on genetic algorithm (GA) was presented synthetically considering the workspace requirement, lowest natural frequency, average frequency and global dimensionally homogeneous Jacobian matrix condition number. An optimal result was obtained through standard GA using penalty function and the Pareto-optimal set was also obtained through parallel selection method.