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.

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.

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.

A Family of 3-DOF Translational Parallel Manipulators1

2003 ◽  
Vol 125 (2) ◽  
pp. 302-307 ◽  
Author(s):  
Marco Carricato ◽  
Vincenzo Parenti-Castelli
Keyword(s):  
Degrees Of Freedom ◽  
Translational Motion ◽  
Parallel Manipulators ◽  
Geometric Interpretation ◽  
The Other ◽  
Six Degrees Of Freedom ◽  
Revolute Joints ◽  
Rotational Degrees Of Freedom

This article addresses parallel manipulators with fewer than six degrees of freedom, whose use may prove valuable in those applications in which a higher mobility is uncalled for. In particular, a family of 3-dof manipulators containing only revolute joints or at the most revolute and prismatic ones is studied. Design and assembly conditions sufficient to provide the travelling platform with a pure translational motion are determined and two sub-families that fulfill the imposed constraint are found: one is already known in the literature, while the other is original. The new architecture does not exhibit rotation singularities, i.e., configurations in which the platform gains rotational degrees of freedom. A geometric interpretation of the translation singularities is provided.

Kinematic calibration of serial robot using dual quaternions

2019 ◽  
Vol 46 (2) ◽  
pp. 247-258 ◽  
Author(s):  
Guozhi Li ◽  
Fuhai Zhang ◽  
Yili Fu ◽  
Shuguo Wang
Keyword(s):  
Kinematic Analysis ◽  
Quaternion Algebra ◽  
Error Model ◽  
Kinematic Calibration ◽  
Dual Quaternion ◽  
Robot Calibration ◽  
Geometrical Meaning ◽  
Content Type ◽  
Dual Quaternions ◽  
Serial Robot

Purpose The purpose of this paper is to propose an error model for serial robot kinematic calibration based on dual quaternions. Design/methodology/approach The dual quaternions are the combination of dual-number theory and quaternion algebra, which means that they can represent spatial transformation. The dual quaternions can represent the screw displacement in a compact and efficient way, so that they are used for the kinematic analysis of serial robot. The error model proposed in this paper is derived from the forward kinematic equations via using dual quaternion algebra. The full pose measurements are considered to apply the error model to the serial robot by using Leica Geosystems Absolute Tracker (AT960) and tracker machine control (T-MAC) probe. Findings Two kinematic-parameter identification algorithms are derived from the proposed error model based on dual quaternions, and they can be used for serial robot calibration. The error model uses Denavit–Hartenberg (DH) notation in the kinematic analysis, so that it gives the intuitive geometrical meaning of the kinematic parameters. The absolute tracker system can measure the position and orientation of the end-effector (EE) simultaneously via using T-MAC. Originality/value The error model formulated by dual quaternion algebra contains all the basic geometrical parameters of serial robot during the kinematic calibration process. The vector of dual quaternion error can be used as an indicator to represent the trend of error change of robot’s EE between the nominal value and the actual value. The accuracy of the EE is improved after nearly 20 measurements in the experiment conduct on robot SDA5F. The simulation and experiment verify the effectiveness of the error model and the calibration algorithms.

scholarly journals Automated Generation of Linkage Loop Equations for Planar One Degree-of-Freedom Linkages, Demonstrated up to 8-Bar

2015 ◽  
Vol 7 (1) ◽  
Author(s):  
Brian E. Parrish ◽  
J. Michael McCarthy ◽  
David Eppstein
Keyword(s):  
Kinematic Analysis ◽  
Degree Of Freedom ◽  
Common Edge ◽  
Adjacency Graph ◽  
Automated Generation ◽  
Cycle Basis ◽  
Revolute Joints

In this paper, we present an algorithm that automatically creates the linkage loop equations for planar one degree of freedom, 1DOF, linkages of any topology with revolute joints, demonstrated up to 8 bar. The algorithm derives the linkage loop equations from the linkage adjacency graph by establishing a rooted cycle basis through a single common edge. Divergent and convergent loops are identified and used to establish the fixed angles of the ternary and higher links. Results demonstrate the automated generation of the linkage loop equations for the nine unique 6-bar linkages with ground-connected inputs that can be constructed from the five distinct 6-bar mechanisms, Watt I–II and Stephenson I–III. Results also automatically produced the loop equations for all 153 unique linkages with a ground-connected input that can be constructed from the 71 distinct 8-bar mechanisms. The resulting loop equations enable the automatic derivation of the Dixon determinant for linkage kinematic analysis of the position of every possible assembly configuration. The loop equations also enable the automatic derivation of the Jacobian for singularity evaluation and tracking of a particular assembly configuration over the desired range of input angles. The methodology provides the foundation for the automated configuration analysis of every topology and every assembly configuration of 1DOF linkages with revolute joints up to 8 bar. The methodology also provides a foundation for automated configuration analysis of 10-bar and higher linkages.

Kinematic Analysis of a HHSHH Spatial Mechanism by Generated Surfaces

2018 ◽  
Vol 5 (2) ◽  
pp. 5289-5295
Author(s):  
P.S.S. Murthy ◽  
A. Satyadevi ◽  
A. Gopala Krishna
Keyword(s):  
Kinematic Analysis ◽  
Spatial Mechanism
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