Theoretical Study On Screw Rolling Between And Distribution Regularity Of Fixed And Moving Axodes Traced By Parallel Mechanisms

The axode is the expanded counterpart of the centrode in Euclidean three-space and widely exists in the close coupling of rotation and translation of PMs(parallel mechanism).This close coupling motion can be described by the screw rolling between moving and fixed axodes of PMs.Based on the Frenet frame of axodes and the motion transmission principle of PM,this thesis develops the kinematic model of the screw rolling between fixed and moving axodes of PM,aiming to reveal its principle of motion and to pro-vide theoretical foundations for the establishment of the performance evaluation system and performance optimization algorithm based on the kinematic invariants of axodes.In addition,for exploring the distribution of rotational axes of PMs,this thesis systematically studies the distribution regularity of screw axes of the general three-system of screws in Euclidean three-space to provide an essential theory for the axode and motion planning of PM.The main research contents are as follows:After constructing Frenet frames on fixed and moving axodes,respectively,this the-sis derives a matrix equation which composites two continuous rigid motions of the Frenet frame on a moving axode relative to the body frame and of the Frenet frame on the conju-gate fixed axode relative to the reference frame,to a continuous rigid motion of the body frame relative to the reference frame.This matrix equation is termed the screw rolling equation of axodes and is proved by three classes of four-bar mechanisms.Based on the tangent operator of the multi-parameter rigid motion,this thesis pre-sents the mathematical definition and the physical means of proper basis screw.This thesis clarifies the motion transmission principle of PM based on the concepts of proper basis screw and generalized transmission wrench screw.Based on the motion transmission pro-cedure and the reciprocal screw theory,this thesis develops an algebraic method to deter-mine the multi-parameter ISAs.After introducing the envelope proper basis screw axodes,this thesis decomposes the screw rolling between fixed and moving resulting IS axodes into the linear superposition of coupling screw rollings between several pairs of fixed and moving envelope proper basis screw axodes.The above methods and equations are proved by the numerical simples of SP+SPR+SPU PM and 3-UPU PM.Based on the relationship between the curves in the graph of the velocity-ratio parameter and the shape of axodes of a 3-UPU PM,this thesis studies the relationship between its motion characteristics and its driving methods.This thesis presents the mathematical expressions of the densest distribution zone of the∞~2 screw axes of the general three-system by deriving the∞~3striction points on them when every screw axis is infinitely close to its surrounding~1∞screw axes in its infinitesi-mal neighborhood space.Studying the~1∞decomposition methods of the general three-system into~1∞general two-subsystems,this thesis reveals the relationship between the densest distribution zone and the cylindroid.In pursuit of a generalized decomposition method,this thesis proposes the general decomposition unit:varying-pitch ruled surface based on the pith-hyperboloid.A numerical example of the 3-RPS pyramid mechanism is presented for the primary application of the concept:the densest distribution zone to the axode planning.This thesis formulates the derivation procedure of the parametric equation of general cycloid by transforming its generation principle to the screw rolling between a pair of par-ticular moving and fixed axodes and then using the screw rolling equation of axodes,to find a simple and general method for the derivation of the parametric equation of general cycloid.