Reconfiguration Analysis of Multimode Single-Loop Spatial Mechanisms Using Dual Quaternions

2017 ◽  
Vol 9 (5) ◽  
Author(s):  
Xianwen Kong
Keyword(s):  
Algebraic Geometry ◽  
Single Degree Of Freedom ◽  
Plane Symmetric ◽  
Dual Quaternions ◽  
Revolute Joints ◽  
Spatial Mechanisms ◽  
Reconfigurable Mechanisms ◽  
Motion Modes ◽  
Kinematic Loop ◽  
And Robotics

Although kinematic analysis of conventional mechanisms is a well-documented fundamental issue in mechanisms and robotics, the emerging reconfigurable mechanisms and robots pose new challenges in kinematics. One of the challenges is the reconfiguration analysis of multimode mechanisms, which refers to finding all the motion modes and the transition configurations of the multimode mechanisms. Recent advances in mathematics, especially algebraic geometry and numerical algebraic geometry, make it possible to develop an efficient method for the reconfiguration analysis of reconfigurable mechanisms and robots. This paper first presents a method for formulating a set of kinematic loop equations for mechanisms using dual quaternions. Using this approach, a set of kinematic loop equations of spatial mechanisms is composed of six polynomial equations. Then the reconfiguration analysis of a novel multimode single-degree-of-freedom (1DOF) 7R spatial mechanism is dealt with by solving the set of loop equations using tools from algebraic geometry. It is found that the 7R multimode mechanism has three motion modes, including a planar 4R mode, an orthogonal Bricard 6R mode, and a plane symmetric 6R mode. Three (or one) R (revolute) joints of the 7R multimode mechanism lose their DOF in its 4R (or 6R) motion modes. Unlike the 7R multimode mechanisms in the literature, the 7R multimode mechanism presented in this paper does not have a 7R mode in which all the seven R joints can move simultaneously.

Kinematic Analysis of Conventional and Multi-Mode Spatial Mechanisms Using Dual Quaternions

2016 ◽  
Author(s):  
Xianwen Kong
Keyword(s):  
Algebraic Geometry ◽  
Kinematic Analysis ◽  
Fundamental Issue ◽  
Input Output ◽  
Plane Symmetric ◽  
Spatial Mechanism ◽  
Dual Quaternions ◽  
Reconfigurable Mechanisms ◽  
Kinematic Loop ◽  
Multi Mode

Although kinematic analysis of conventional mechanisms is a well-documented fundamental issue in mechanisms and robotics, the emerging reconfigurable mechanisms and robots (or mechanisms and robots with multiple operation modes) require re-examining this fundamental issue. Recent advances in mathematics, especially algebraic geometry and numerical algebraic geometry, make it possible to develop an efficient method for the kinematic analysis of not only conventional mechanisms and robots but also reconfigurable mechanisms and robots. This paper first presents a method for setting up a set of kinematic loop equations for mechanisms using dual quaternions. Using this approach, a set of kinematic loop equations of a spatial mechanism is composed of six equations. The effectiveness of the proposed kinematic loop equations is then demonstrated by deriving the explicit input-output equations of a line symmetric 1-DOF (degree-of-freedom) 7R single-loop spatial mechanism, the re-configuration analysis of a novel multi-mode 1-DOF 7R spatial mechanism. In the former case, an explicit input-output equation of degree 8 is derived. In the latter case, it is found that the 7R multi-mode mechanism has three motion modes, including a planar 4R mode, an orthogonal Bricard 6R mode, and a plane symmetric 6R mode. Unlike the 7R multi-mode mechanisms in the literature, the 7R multi-mode mechanism presented in this paper does not have a 7R mode in which all the seven R joints can move simultaneously.

Synthesis of Spatial Two-Link Coupled Serial Chains

1998 ◽  
Author(s):  
Venkat Krovi ◽  
G. K. Ananthasuresh ◽  
Vijay Kumar
Keyword(s):  
Path Following ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Single Degree Of Freedom ◽  
End Effector ◽  
Revolute Joints ◽  
Spatial Mechanisms ◽  
Serial Chain ◽  
Serial Chains ◽  
Selection Of

Abstract We address the synthesis of serial chain spatial mechanisms with revolute joints in which the rotations about the joints are coupled via cables and pulleys. Such coupled serial chain mechanisms offer a middle ground between the more versatile and compact serial chains and the simpler closed chains by combining some of the advantages of both types of systems. In particular, we focus on the synthesis of single degree-of-freedom, coupled serial chains with two revolute joints. We derive precision point synthesis equations for two precision points by combining the loop closure equations with the necessary geometric constraints in terms of the unknown mechanism parameters. This system of equations can now be solved linearly for the link vectors after a suitable selection of free choices. We optimize over the free choices to generate an end effector trajectory that closely approximates a desired end effector trajectory for motion generation and path following applications.

A Single-Loop 7R Spatial Mechanism That Has Three Motion Modes With the Same Instantaneous DOF but Different Finite DOF

2018 ◽  
Author(s):  
Xianwen Kong ◽  
Andreas Müller
Keyword(s):  
Higher Order ◽  
Mobility Analysis ◽  
Single Loop ◽  
Plane Symmetric ◽  
Spatial Mechanism ◽  
Motion Modes ◽  
Regular Configuration ◽  
Kinematic Loop ◽  
Multi Mode ◽  
Motion Mode

Multi-mode mechanisms, including kinematotropic mechanisms, are a class of reconfigurable mechanisms that can switch motion modes with the same or different DOF (degree-of-freedom). For most of the multi-mode mechanisms reported in the literature, the instantaneous (or differential) DOF and finite DOF in a motion mode are equal. In this paper, we will discuss the construction, reconfiguration analysis, and higher-order mobility analysis of a multi-mode single-loop 7R mechanism that has three motion modes with the same instantaneous DOF but different finite DOF. Firstly, the novel multi-mode single-loop 7R spatial mechanism is constructed by inserting one revolute (R) joint into a plane symmetric Bennett joint-based 6R mechanism for circular translation. The reconfiguration analysis is then carried out in the configuration space by solving a set of kinematic loop equations based on dual quaternions and the natural exponential function substitution using tools from algebraic geometry. The analysis shows that the multi-mode single-loop 7R spatial mechanism has three motion modes, including a 2-DOF planar 5R mode and two 1-DOF spatial 6R modes and can transit between each pair of motion modes through two transition configurations. The higher-order mobility analysis shows that the 7R mechanism has two-instantaneous DOF at a regular configuration of any motion mode and three instantaneous DOF in a transition configuration. The infinitesimal motions that are not tangential to finite motions are of second-order in transition configurations between 2-DOF motion mode 1 and 1-DOF motion modes 2 or 3 or first-order in transition configurations between 1-DOF motion modes 2 and 3.

Variable degree-of-freedom spatial mechanisms composed of four circular translation joints

2021 ◽  
pp. 1-16
Author(s):  
Xianwen Kong
Keyword(s):  
Algebraic Geometry ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Variable Degree ◽  
Circular Trajectory ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
Motion Modes ◽  
Multi Mode ◽  
Motion Mode

Abstract This paper deals with the construction and reconfiguration analysis of a spatial mechanism composed of four circular translation (G) joints. Two links connected by a G joint, which can be in different forms such as a planar parallelogram, translate along a circular trajectory with respect to each other. A spatial 4G mechanism, which is composed of four G joints, usually has 1-DOF (degree-of-freedom). Firstly, a 2-DOF spatial 4G mechanism is constructed. Then a novel variable-DOF spatial 4G mechanism is constructed starting from the 2-DOF 4G mechanism using the approach based on screw theory. Finally, the reconfiguration analysis is carried out in the configuration space using dual quaternions and tools from algebraic geometry. The analysis shows that the variable-DOF spatial 4G mechanism has one 2-DOF motion mode and one to two 1-DOF motion modes and reveals how the 4G mechanism can switch among these motion modes. By removing one link from two adjacent G joints each and two links from each of the remaining two G joints, we can obtain a queer-rectangle and a queer-parallelogram, which are the generalization of the queer-square or derivative queer-square in the literature. The approach in this paper can be extended to the analysis of other types of coupled mechanisms using cables and gears and multi-mode spatial mechanisms involving G joints.

Type Synthesis of Single-Loop Overconstrained 6R Spatial Mechanisms for Circular Translation

2014 ◽  
Vol 6 (4) ◽  
Author(s):  
Xianwen Kong
Keyword(s):  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Single Loop ◽  
Plane Symmetric ◽  
Research Areas ◽  
Revolute Joints ◽  
Spatial Mechanisms ◽  
Special Cases ◽  
Overconstrained Mechanisms ◽  
Self Motion

To discover single-degree-of-freedom (DOF) single-loop overconstrained mechanisms is still an open problem. This paper deals with the type synthesis of single DOF single-loop overconstrained 6RMCTs (6R spatial mechanisms for circular translation). These mechanisms provide alternatives to planar parallelograms and are also associated with self-motion of several translational parallel mechanisms. 6RMCTs are to be obtained using a construction approach in combination with the approaches to the type synthesis of parallel mechanisms. By imposing certain conditions on the hybrid overconstrained 6R (plano-spherical, plano-Bennett, double-spherical, and spherico-Bennett) mechanisms, Bricard plane symmetric mechanism, and Bricard line symmetric mechanism, six special cases of 6RMCTs are obtained. By combining planar parallelograms with these special mechanisms, the general cases of 6RMCTs are then constructed. Finally, 4R2H, 2R4H, and 6H mechanisms for circular translation are obtained from the above 6RMCTs by replacing one or more pairs of R (revolute) joints with parallel axes each with a pair of H (helical) joints with parallel axes and the same pitch. This work contributes to the research on overconstrained six-bar mechanisms and further reveals that the research areas of parallel mechanisms and single-loop overconstrained mechanisms are closely related.

A Method for Type Synthesis of Mechanisms Using Phase Diagrams

1994 ◽  
Author(s):  
Sio-Hou Lei ◽  
Ying-Chien Tsai
Keyword(s):  
Phase Diagram ◽  
Degrees Of Freedom ◽  
Practical Application ◽  
Type Synthesis ◽  
Planar Mechanisms ◽  
Simple Loop ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Spatial Mechanisms ◽  
Synthesis Of Mechanisms

Abstract A method for synthesizing the types of spatial as well as planar mechanisms is expressed in this paper by using the concept of phase diagram in metallurgy. The concept represented as a type synthesis technique is applied to (a) planar mechanisms with n degrees of freedom and simple loop, (b) spatial mechanisms with single degree of freedom and simple loop, to enumerate all the possible mechanisms with physically realizable kinematic pairs. Based on the technique described, a set of new reciprocating mechanisms is generated as a practical application.

Kinematic Analysis of Spatial Mechanisms by Means of Screw Coordinates. Part 2—Analysis of Spatial Mechanisms

1971 ◽  
Vol 93 (1) ◽  
pp. 67-73 ◽  
Author(s):  
M. S. C. Yuan ◽  
F. Freudenstein ◽  
L. S. Woo
Keyword(s):  
Computer Program ◽  
Kinematic Analysis ◽  
Static Force ◽  
Single Degree Of Freedom ◽  
Numerical Examples ◽  
Spatial Mechanism ◽  
Single Degree ◽  
Spatial Mechanisms ◽  
Torque Analysis ◽  
Basic Concepts

The basic concepts of screw coordinates described in Part I are applied to the numerical kinematic analysis of spatial mechanisms. The techniques are illustrated with reference to the displacement, velocity, and static-force-and-torque analysis of a general, single-degree-of-freedom spatial mechanism: a seven-link mechanism with screw pairs (H)7. By specialization the associated computer program is capable of analyzing many other single-loop spatial mechanisms. Numerical examples illustrate the results.

scholarly journals Four-Pose Synthesis of Angle-Symmetric 6R Linkages

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Gábor Hegedüs ◽  
Josef Schicho ◽  
Hans-Peter Schröcker
Keyword(s):  
Rotation Angle ◽  
Dual Quaternions ◽  
Revolute Joints ◽  
Factorization Theory ◽  
Theory Of Motion ◽  
Kinematic Loops ◽  
Parametric Families ◽  
Synthesis Approach ◽  
Relative Motions

We use the recently introduced factorization theory of motion polynomials over the dual quaternions and cubic interpolation on quadrics for the synthesis of closed kinematic loops with six revolute joints that visit four prescribed poses. The resulting 6R linkages are special in the sense that the relative motions of all links are rational. They exhibit certain elegant properties such as symmetry in the rotation angles and, at least in theory, full-cycle mobility. Our synthesis approach admits either no solution or two one-parametric families of solutions. We suggest strategies for picking good solutions from these families. They ensure a fair coupler motion and optimize other linkage characteristics such as total rotation angle or linkage size. A comprehensive synthesis example is provided.

A New Family of Bricard-Derived Deployable Mechanisms

2016 ◽  
Vol 8 (3) ◽  
Author(s):  
Hailin Huang ◽  
Bing Li ◽  
Jianyang Zhu ◽  
Xiaozhi Qi
Keyword(s):  
Large Volume ◽  
Computer Aided Design ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
New Family ◽  
Revolute Joints ◽  
Computer Aided ◽  
Cad Models ◽  
Aided Design

This paper proposes a new family of single degree of freedom (DOF) deployable mechanisms derived from the threefold-symmetric deployable Bricard mechanism. The mobility and geometry of original threefold-symmetric deployable Bricard mechanism is first described, from the mobility characterstic of this mechanism, we show that three alternate revolute joints can be replaced by a class of single DOF deployable mechanisms without changing the single mobility characteristic of the resultant mechanisms, therefore leading to a new family of Bricard-derived deployable mechanisms. The computer-aided design (CAD) models are used to demonstrate these derived novel mechanisms. All these mechanisms can be used as the basic modules for constructing large volume deployable mechanisms.

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