Geometric Morphology Of Screw Systems And Design Of Reconfigurable Mechanisms

In the 21^st century,humankind are facing a complex and changeable environment,various working conditions and increasing demands.This results in the rise of reconfigurable mechanisms as a filed established by Dai early in this century.This thesis focuses on analysis and design of reconfigurable mechanisms based on screw systems theory and kinematic curves theory.The thesis will research on the geometric morphologies of screw systems and characteristics of kinematic curve.Further it will analyze the reconfigurability of existing mechanisms and design new reconfigurable mechanisms to meet the requirements.As an important theoretical basis,the screw system theory plays a crucial role in the research of mechanisms and robotics.This thesis gives two new geometric morphologies of screw system of the third order with zero pitch based on the concept of ruled surface.These geometric morphologies are unified with the quadric surface using the duality of the surface.The result is further extended to the screw system of the third order with the same nonzero pitch.Using the interrelationship between the screw systems and corresponding reciprocal screw systems,the derivation of the geometric morphology is given for screw systems of higher order.Based on screw system theory,this thesis analyzes the motion and reconfigurability of a reconfigurable linkage from a kirigami.The linkage is proved to have two spherical motion branches and one planar motion branch.The three motion branches further result in spherical motion and planar motion for points on the linkage.The transition indexes are obtained to describe the reconfigurability of the linkage and they are used to design new reconfigurable linkages.Thus,three new reconfigurable linkages are presented.The three reconfigurable linkages accomplish transformations between three different geometric morphologies of screw system of the third order.Based on the concept of double points and tangent lines in the algebraic curve theory,a necessary condition is given for the partial derivatives of the kinematic curve when the linkage is at the bifurcation point.Using the higher order partial derivatives,the thesis further gives a sufficient condition for the linkage having bifurcation motion at the required joint parameters.Then the RCRCR linkage is designed to have bifurcation motion at the given joint parameters.Using Myard plane-symmetric 6R linkage and Myard plane-symmetric 5R linkage,the singularity point and the bifurcation point are distinguished with the help of the necessary condition.This results in a new reconfigurable RURU linkage and a new reconfigurable 4R linkage.Both of the two new reconfigurable linkages are able to have bifurcation motion at singularity points.Using the necessary condition,Bricard line-symmetric 6R linkage is further analyzed and two new reconfigurable linkages are presented.One linkage has two different Bricard line-symmetric 6R motion branches and the other linkage has two Bricard line-symmetric 6R motion branches and one Bennett motion branch.Based on configuration torus,the thesis deals with the special motion cycle of linkages.When the bifurcation motion occurs,the motion cycle of the linkage cannot be accomplished in one joint-revolution.This results in the extending motion cycle for the linkage.It happens even for the linkage without bifurcation motion.By mapping the kinematic curve to the configuration torus,the motion cycle of Bennett plano-spherical hybrid linkage is proved to be four times of joint-revolutions and the bifurcation points of the linkage becomes the self-intersection point on the configuration torus.The motion cycle of Myard plane-symmetric 5R linkage is twice of joint-revolutions on the configuration torus,but there is no bifurcation motion for the linkage.The spherical 4R linkage is designed to have bifurcation motion and its motion cycle is twice of joint-revolutions for one motion branch.