Type Synthesis of 4-DOF Parallel Kinematic Mechanisms Based on Grassmann Line Geometry and Atlas Method

Many methods are proposed to deal with the type synthesis of parallel kinematic mechanisms（PKMs）, but most of them are less intuitive to some extent. Thus, to propose a concise and intuitive type synthesis method for engineering application is a very challenging issue, which should be further studied in the field. Grassmann line geometry, which can investigate the dimensions of spatial line-clusters in a concise way, is taken as the mathematic foundation. Atlas method is introduced to visually describe the degrees of freedom（DOFs） and constraints of a mechanism, and the dual rule is brought in to realize the mutual conversion of the freedom-space and constraint-space. Consequently, a systematic method based on Grassmann line geometry and Atlas method is generated and the entire type synthesis process is presented. Three type 4-DOF PKMs, i.e., 1T3R, 2T2R and 3T1R（T： translational DOF; R： rotational DOF）, are classified according to the different combinations of the translational DOFs and rotational DOFs. The type synthesis of 4-DOF PKMs is carried out and the possible configurations are thoroughly investigated. Some new PKMs with useful functions are generated during this procedure. The type synthesis method based on Grassmann line geometry and Atlas method is intuitive and concise, and can reduce the complexity of the PKMs＇ type synthesis. Moreover, this method can provide theoretical guidance for other PKMs＇ type synthesis and engineering application. A novel type synthesis method is proposed, which solves the existing methods＇ problems in terms of complicated, not intuitive and unsuitable for practical application.

An Iteration Method Based on Homotopy Function for Solving Polynomial Systems and Application to Mechanisms Problems

A new iterating method based on homotopy function is developed in this paper. All solutions can be found easily without the need of choosing proper initial values. Compared to the homotopy continuation method, the solution process of the present method is simplified, and the computation efficiency as well as the reliability for obtaining all solutions is also improved. By application of the method to the mechanisms problems, the results are satisfactory.

Establishment of Knowledge Base Management System and the Type Selection of Mechanism for Mechanism Kinematic Scheme

Firstly data standardization technology and combined classification method have been applied to carry out classification of kinematic behaviors and mechanisms in the mapping field between the kinematic behavior level and the mechanism level of conceptual design.The principle of computer coding and storing have been built to give a fast and broad selection of mechanisms that meets the requirements of basic motion characters.Then on the basis of mentioned above,the heuristic matching propagation principle (HMPP) of kinematic behaviors and its true table serves as a guide to perform mechanism types selection.Finally an application is given to indicate its practicability and effectiveness.

KINEMATIC ANALYSIS OF THE GENERAL SPATIAL 7R MECHANISM

The displacement, velocity and acceleration analysis of the general spatial 7R mechanism is discussed in this paper, fused on the method proposed in Ref. [2], an input-output algebra equation of the 16th degree in the tan-half-angle of the output angular displacement is derived. The derivation process and computation are considerably simple. A program written in Allanguage is used to derive the coefficients of displacement equations: therefore the amount of manual work is greatly decreased. The results are verified by a numerical example. The researches of this paper and Ref. [5]found a base for establishing an expert system of spatial mechanism analysis in the future.

Rigid Subchain Detection Algorithm of Mechanism Kinematic Chain and Realization of Recursive Program

In the process of kinematic chain type synthesis,it is necessary to solve the problems of isomorphism identification and rigid subchain detection.The problem of rigid subchain detection can be reduced to subgraph isomorphism problem,which belongs to NPC problem.This paper introduces the properties,detection methods,algorithm time complexity and program code of rigid subchain of kinematic chain.The detection codes of rigid subchains with different number of links are different.It is necessary to modify the for-loop nesting times of program code according to the change of the link number,so the code reusability is very low.In view of this,the recursive pseudo code of rigid subchain detection algorithm is proposed for the first time,which makes the program can be directly used for rigid subchain detection of any number of links,improves the reusability of the code,and provides a certain reference for the realization and optimization of computer programs for NPC problems in other disciplines.A rigid subchain detection software of kinematic chain was developed,and the rigid subchain detection process of a 16-link kinematic chain was successfully realized in the software.

Research on Novel Linear Driving and Metamorphic Characteristics for Slider-actuated Parallel (Hybrid) Mechanism

This paper presents a novel one-axis linear-drive control system, in which wire rope is wound orderly around drum by servo motor drive and drays the working slider for a long linear reciprocating motion. PKM with this control system is metamorphic and can achieve great feed forces, accelerations and transverse speeds, high accuracy and low cost. The metamorphic characteristics are studied, including the metamorphic condition, con- tents, process as well as procedures. The kinematics computation model is established and analyzed.

Introduction to Synchronized Kinematic and Electromagnetic Mechanics

Introduction to fundamental physics according to the parallel harmonization of kinematic and electromagnetic mechanics, in accordance with Wilhelm Wien’s project, which involved the integration in kinematic mechanics of the mass increase of the electron as a function of its velocity, as measured by Walter Kaufmann with his bubble-chamber experiments, and analyzed and confirmed by H. A. Lorentz and all the leading edge physicists who then re-analyzed this data.

Accuracy Analysis for 6-DOF PKM with Sobol Sequence Based Quasi Monte Carlo Method

To improve the precisions of pose error analysis for 6-dof parallel kinematic mechanism( PKM)during assembly quality control,a Sobol sequence based on Quasi Monte Carlo( QMC) method is introduced and implemented in pose accuracy analysis for the PKM in this paper. The Sobol sequence based on Quasi Monte Carlo with the regularity and uniformity of samples in high dimensions,can prevail traditional Monte Carlo method with up to 98. 59% and 98. 25% enhancement for computational precision of pose error statistics.Then a PKM tolerance design system integrating this method is developed and with it pose error distributions of the PKM within a prescribed workspace are finally obtained and analyzed.

Forward Displacement Analysis of a Class of the 6-6 Stewart Platforms

A special form of the Stewart platform is presented in which the top platform and base platform are similar and corresponding vertices are connected by six prismatic joints.A closed-from solution for the forward displacement analysis of this mechanism is developed.When the six vertices of the top platform are in a quadratic curve,this mechanism becomes singular.This new theoretical result is confirmed with a numerical example.

Workshop Oriented Tolerance Synthesis for Spatial PKM

To promote the pose accuracy performance of a spatial parallel kinematic Mechanism( PKM) in service,a workshop oriented tolerance synthesis method based on design of experiment( DOE) is proposed,which involves two consecutive stages. In the first stage of DOE,the tolerance factor sensitivities are obtained according to initial tolerance settings with the consideration of the current manufacturing capacity,and the second stage of DOE makes use of them to produce multiple tolerance allocations which can adapt to current manufacturing capacity. A tolerance synthesis procedure is developed and integrated in tolerance design system for PKM. Comparing the results with peer method,the validity and practicability of this method is verified.

Application of Parallel Mechanism in Varistructured Quadruped/Biped Human-carrying Walking Chair Robot

For the existing problems of walking chair robot such as simple function,lower bearing capacity and not walking in complex environment,a novel varistructured quadruped / biped human-carrying walking chair robot is proposed.The proposed robot could be used as biped and quadruped walking chair robots.Considering the conversion of the walking chair robot from the quadruped to the biped or vice versa,6-UPS and 2-UPS＋UP（U,P and S are universal joint,the prismatic pair,and sphere joint,respectively） parallel mechanisms are selected as the leg mechanism of the biped walking robot and quadruped walking robot,respectively.Combining the screw theory and theory of mechanism,the degrees of freedom of the leg mechanism and the body mechanism in diferent motion states are computed so as to meet the requirements of mechanism design.The motion characteristics of the 2-UPS＋UP parallel mechanism which is the key part of the walking chair robot are analyzed.Then,the workspace of the moving platform is drawn and the efect of the structural parameters on the workspace volume is studied.Finally,it is found that the volume of the workspace of the moving platform is bigger when the side length ratio and the vertex angle ratio of the fxed platform and the moving platform which are isosceles triangles are close to 1.This study provides a theoretical foundation for the prototype development.