A Double-Faced 6R Single-Loop Overconstrained Spatial Mechanism

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Xianwen Kong ◽  
Xiuyun He ◽  
Duanling Li
Keyword(s):  
Kinematic Analysis ◽  
Isosceles Triangle ◽  
The Other ◽  
Dual Quaternion ◽  
Single Loop ◽  
Plane Symmetric ◽  
Spatial Mechanism ◽  
Revolute Joints ◽  
Full Turn ◽  
Overconstrained Mechanisms

This paper deals with a 6R single-loop overconstrained spatial mechanism that has two pairs of revolute joints with intersecting axes and one pair of revolute joints with parallel axes. The 6R mechanism is first constructed from an isosceles triangle and a pair of identical circles. The kinematic analysis of the 6R mechanism is then dealt with using a dual quaternion approach. The analysis shows that the 6R mechanism usually has two solutions to the kinematic analysis for a given input and may have two circuits (closure modes or branches) with one or two pairs of full-turn revolute joints. In two configurations in each circuit of the 6R mechanism, the axes of four revolute joints are coplanar, and the axes of the other two revolute joints are perpendicular to the plane defined by the above four revolute joints. Considering that from one configuration of the 6R mechanism, one can obtain another configuration of the mechanism by simply renumbering the joints, the concept of two-faced mechanism is introduced. The formulas for the analysis of plane symmetric spatial triangle are also presented in this paper. These formulas will be useful for the design and analysis of multiloop overconstrained mechanisms involving plane symmetric spatial RRR triads.

A 6R Single-Loop Overconstrained Spatial Mechanism That Has Two Pairs of Revolute Joints With Intersecting Axes and One Pair of Revolute Joints With Parallel Axes

2017 ◽  
Author(s):  
Xianwen Kong ◽  
Xiuyun He ◽  
Duanling Li
Keyword(s):  
Kinematic Analysis ◽  
Isosceles Triangle ◽  
The Other ◽  
Dual Quaternion ◽  
Single Loop ◽  
Spatial Mechanism ◽  
Revolute Joints ◽  
Full Turn

This paper deals with a 6R single-loop overconstrained spatial mechanism that has two pairs of revolute joints with intersecting axes and one pair of revolute joints with parallel axes. The 6R mechanism is first constructed from an isosceles triangle and a pair of identical circles. The kinematic analysis of the 6R mechanism is then dealt with using a dual quaternion approach. The analysis shows that the 6R mechanism usually has two solutions to the kinematic analysis for a given input and may have two circuits (closure modes or branches) with one or two pairs of full-turn revolute joints. In two configurations in each circuit of the 6R mechanism, the axes of four revolute joints are coplanar, and the axes of the other two revolute joints are perpendicular to the plane defined by the above four revolute joints. Considering that from one configuration of the 6R mechanism, one can obtain another configuration of the mechanism by simply renumbering the joints, the concept of two-faced mechanism is introduced.

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.

Overconstrained Analysis of Five-Link Spatial Single Loops With Revolute and Prismatic Joints

2000 ◽  
Author(s):  
Qiong Jin ◽  
Lu-Bin Hang ◽  
Ming Zhang
Keyword(s):  
Theoretical Basis ◽  
The Other ◽  
New Method ◽  
Input Output ◽  
Displacement Analysis ◽  
Single Loop ◽  
Prismatic Joints ◽  
Existence Conditions ◽  
Closure Conditions ◽  
Overconstrained Mechanisms

Abstract A new method on determining the existence conditions of overconstrained mechanisms is presented in this paper, which is used for studying the spatial single loop generally possessing one configure. This method is very effective to distinguish finite and infinite solutions of displacement analysis, and can analytically deduce the input-output equations. It is elucidated that the existence conditions of overconstrained mechanism consist of the overconstrained conditions and the closure conditions, and that the independence of the closure conditions should be further discussed. On the other hand, the existence conditions of two known 5-link overconstrainded mechanisms are verified and corrected. This method also provides a theoretical basis for finding new oveconstrained mechanisms.

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.

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.

Kinematic design and motion analysis of spatial rapier drive mechanisms used in weaving machines

2014 ◽  
Vol 84 (19) ◽  
pp. 2065-2073 ◽  
Author(s):  
Recep Eren ◽  
Mesrur Erturk ◽  
Barıs Hascelik
Keyword(s):  
Motion Analysis ◽  
Kinematic Analysis ◽  
Gear Ratio ◽  
Main Shaft ◽  
Drive Mechanism ◽  
Spatial Mechanism ◽  
Kinematic Design ◽  
Shaft Angle

This paper presents an approach for the kinematic design of a rapier drive mechanism containing a spatial mechanism and analyses rapier motion curve. Kinematic design and analysis equations are derived and then the link lengths of the spatial mechanism are calculated in order to satisfy the critical rapier positions inside and outside the shed. In this way, the portions of one loom revolution, during which the rapiers are inside and outside the shed, are determined. The rapier motion curve is obtained by using kinematic analysis equations. It is shown that the position of the oscillating link in the spatial mechanism and the loom main shaft angle at which the rapier enters the shed have the most significant effect on the rapier motion curve. The gear ratio has also some effect on the rapier motion curve. Different rapier motion curves are obtained by changing these parameters and the suitability of these curves for rapier motion is discussed.

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 Kinematic analysis of a single-loop reconfigurable 7R mechanism with multiple operation modes

Robotica ◽  
2014 ◽  
Vol 32 (7) ◽  
pp. 1171-1188 ◽  
Author(s):  
Xiuyun He ◽  
Xianwen Kong ◽  
Damien Chablat ◽  
Stéphane Caro ◽  
Guangbo Hao
Keyword(s):  
Kinematic Analysis ◽  
Computer Aided Design ◽  
Operation Mode ◽  
Algebraic Approach ◽  
Single Loop ◽  
Operation Modes ◽  
Translational Mode ◽  
Kinematic Mapping ◽  
Multiple Operation ◽  
Aided Design

SUMMARYThis paper presents a novel one-degree-of-freedom (1-DOF) single-loop reconfigurable 7R mechanism with multiple operation modes (SLR7RMMOM), composed of seven revolute (R) joints, via adding a revolute joint to the overconstrained Sarrus linkage. The SLR7RMMOM can switch from one operation mode to another without disconnection and reassembly, and is a non-overconstrained mechanism. The algorithm for the inverse kinematics of the serial 6R mechanism using kinematic mapping is adopted to deal with the kinematic analysis of the SLR7RMMOM. First, a numerical method is applied and an example is given to show that there are 13 sets of solutions for the SLR7RMMOM, corresponding to each input angle. Among these solutions, nine sets are real solutions, which are verified using both a computer-aided design (CAD) model and a prototype of the mechanism. Then an algebraic approach is also used to analyse the mechanism and same results are obtained as the numerical one. It is shown from both numerical and algebraic approaches that the SLR7RMMOM has three operation modes: a translational mode and two 1-DOF planar modes. The transitional configurations among the three modes are also identified.

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