Static Analysis Of Three2R1T3-DOF Parallel Mechanisms

Force analysis is an important part of the mechanical design, the statics analysis of threekinds of2R1T Lower-mobility parallel manipulators provides theoretical support for design andengineering application of parallel manipulators.3-PRRU parallel manipulator,2-PRS-PRRU parallel manipulator and2-PRU-PRRU parallelmanipulator are the three kinds of2R1T Lower-mobility parallel manipulators.2-PRU-PRRUhas redundant constrain.By the dismantle-bar method, the static equilibrium equations of the mechanism are set up.Then we can get42equilibrium equations of3-PRRU,30equilibrium equations of2-PRS-PRRU and32equilibrium equations of2-PRU-PRRU. In the32equilibrium equations of2-PRU-PRRU, there are two compatibility equation of deformation. Integrating all theequilibrium equations can get three constraint force transmit motion matrixes. Finally draw theconstraints provided by joints in contour map by Matlab. The constraints changed by theworking space.In order to prove the validity of the whole solution results, given a method of staticsimulation of the three kinds of parallel mechanism by Solidworks Motion. By the matching oflines and point, we can get more close to the theoretical model of the simulation model of joints.The simulation results can be more close to the theoretical results by these method, then theverification will be more accurate.After the verification, studying the force properties assessment of the three kind ofLower-mobility parallel manipulators. To the Lower-mobility parallel manipulators, not onlyconsider the actuation force or moment but also provide constraint force of moment for theirend-effectors. The actuation force properties assessment is more complete than constraint forceproperties assessment, therefore this paper mainly studies three kinds of static load performanceof parallel mechanism. Getting the largest singular value and the minimum singular value bysingular value decomposition(SVD) for the three constraint force transmit motion matrixes.These singular value reflects the capacity of the mechanisms resist the same external loads.Drawing grid map of the three mechanism force properties assessment by Matlab.External load changes also effect on the force properties assessment, now studying the forceproperties assessment in the fixed configuration. Then finding initial, general, and singular configurations, observing the force properties assessments’ changes with the direction of externalload change.