Kinematics Of Spatial Mechanisms And Innovative Design Of Metamorphic Parallel Mechanisms

The kinematics of spatial mechanisms is one of the main and basic topics in the research of robot mechanisms,which gives theoretical support to the real application of robots.This dissertation presents the research work on the kinematics of the general 7R mechanism,general 6-6 Stewart mechanism and general Stewart-Gough platforms,their modeling,theories and solving procedures have been discussed,leading to some new methods.Also metamorphic parallel mechanisms are studied and new designs have been given,their mobility varieties are demonstrated during the topological change by using reciprocal screws.The main contents and contributions can be summarized as follows:(1) Based on the study of dual quaternion theory in modelling of serial mechanisms,the inverse kinematics of the spatial 7R mechanism is analyzed. By using Dixon's resultant with the constraint equations,a 6×6 matrix of which the determinant equals to zero is obtaind,leading to the closed-form input-output 16^th-order equation,numerical examples confirm these theretical results.The whole process is very simple and easy to be programmed,which supplies a new method for the real using of the 7R mechanism.(2) By using Calay's formular,the constraint equations of the forward kinematics of the general 6-6 Stewart mechanism are built,which are reduced to six polynomial equations in three unknown.Gr(o|¨)bner basis theory is used and the problem of the forward displacement results in a 40th degree polynomial equation in a single unknown from a constructed 13×13 Sylvester's matrix which is relatively small in the size,from which 40 different locations of the moving platform can be derived.(3) The general Stewart-Gough platforms produced by Xiaoshan Gao are studied,especially the class that has angle constraints.The forward kinematics is analyzed by choosing one of the mechanisms which have one, two,three or zero angle constraint.Wherein,3-CCC is a new parallel mechanism which has three angle constraints and three distance constraints, Calay's formular and direction cosine matrix are used to describe the rotation matrix respectively.By setting Dixon's and Sylvester's resultant with the three angle constraint equations respectively and using parameters replacement to deal with the distance constraint equations,the 64 order input-output equation of the forward kinematics is obtained under both of the methods.Numerical example confirms these theretical results and the motion simulation is shown in VC++ by integrating OpenGL.While 2CCC-4SPS,a new parallel mechanism that has two angle constraits and four distance constraints,has a 32^nd-order forward-dispacement input-output equation,the forward kinematics of 1CCC-5SPS,a new parallel mechanism that has one angle constrait and five distance constraints,is prooved to have 40 solutions,both are based on Grobner basis theory.6CCS is another new parallel mechanism that has six point-to-line distance constraints and consists of cylindrical joints and spherical joints.By constructing a Dixon's resultant,the forward kinematics for the orientation is reduced to a 64^th-order polynomial equation in one unknown and the position has 8 solutions corresponding to each orientation,totally,the number of the solution of the forward kinematics is 512.Numerical examples confirm these theretical results.(4) Based on studying and improving the traditional Hook's joint,this thesis gives a new design of a three-DOF rT joint.The new rT joint not only has two rotation axes that intersect at right angle,but also has another rotational degree of freedom which can be used to modify the assembly of other joints.This can change the mobility of the parallel mechanisms that assembled with the new rT joints and leads to two types of metamorphic paralllel mechanisms:In the first type,the mechanism changes its topology by turning the new rT joints in all limbs into different configurations which reconfigures the constraints within the limbs or the assembly of all the limb constraints.This change of mobility is completed by two cases.One is illustrated by a 3(rT)PS and a 3(rT)C(rT) parallel mechanism,by altering the rT joint into different configurations there will produce or reduce local degrees of freedom and thus change the constraits to the moving platform.This qualifies the 3(rT)PS and 3(rT)C(rT) to have variable mobility from 3 through to 6 and from 1 through to 6 respectively.Another case is 3(rT)P(rT) parallel mechanism having various configurations including pure translations,pure rotations or mobility 4 under the changing of assembly of all the limb constraints.In the second type,a central strut with the new rT joint is added in the parallel mechanism.The variable mobility of the mechanisms results from the topological change of the central strut.This is illustrated in a 3SPS-1(rT)P(rT) metamorphic parallel mechanism which changes its mobility from 4 to 5.