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.

scholarly journals Automated Generation of Linkage Loop Equations for Planar 1-DoF Linkages, Demonstrated up to 8-Bar

2014 ◽  
Author(s):  
Brian E. Parrish ◽  
J. Michael McCarthy ◽  
David Eppstein
Keyword(s):  
Kinematic Analysis ◽  
Common Edge ◽  
Automated Generation ◽  
Cycle Basis

In this paper we present an algorithm that automatically creates the linkage loop equations for planar 1-DoF linkages of any topology with rotating joints, demonstrated up to 8-bars. The algorithm derives the linkage loop equations from the linkage graph by establishing a 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 five distinct 6-bar mechanisms, Watt I-II and Stephenson I-III, as well as the seventy one 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 1-DoF linkages with rotating joints up to 8-bar. The methodology also provides a foundation for automated configuration analysis of 10-bar and higher linkages.

Kinematic and Workspace Modelling of a 6-PUS Parallel Mechanism

2018 ◽  
Author(s):  
Jérôme Landuré ◽  
Clément Gosselin
Keyword(s):  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Accurate Description ◽  
Transmission Ratio ◽  
Inverse Kinematic Problem ◽  
Jacobian Matrices ◽  
Six Degree Of Freedom

This article presents the kinematic analysis of a six-degree-of-freedom six-legged parallel mechanism of the 6-PUS architecture. The inverse kinematic problem is recalled and the Jacobian matrices are derived. Then, an algorithm for the geometric determination of the workspace is presented, which yields a very fast and accurate description of the workspace of the mechanism. Singular boundaries and a transmission ratio index are then introduced and studied for a set of architectural parameters. The proposed analysis yields conceptual architectures whose properties can be adjusted to fit given applications.

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.

A Novel 3-DOF Parallel Robot and its Kinematic Analysis

2014 ◽  
Vol 607 ◽  
pp. 759-763
Author(s):  
Xiao Bo Liu ◽  
Xiao Dong Yuan ◽  
Xiao Feng Wei ◽  
Wei Ni
Keyword(s):  
Motion Control ◽  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Parallel Robot ◽  
Degree Of Freedom ◽  
The Novel ◽  
Forward Displacement ◽  
Simulation Based ◽  
Simulation Results

This paper deals with the design and analysis of a novel and simple two-translation and one-rotation (3 degrees of freedom, 3-dof) mechanism for alignment. Firstly, degree of freedom of the parallel robot is solved based on the theory of screw. Secondly considering the demand of motion control, we have conducted the analysis on the 3-dof parallel robot, which includes inverse displacement, forward displacement, and simulation based on SolidWorks Motion. The simulation results indicate that the novel 3-dof robot is suitable for performing the required operations.

Forward/Reverse Velocity and Acceleration Analysis for a Class of Lower-Mobility Parallel Mechanisms

2006 ◽  
Vol 129 (4) ◽  
pp. 390-396 ◽  
Author(s):  
Si J. Zhu ◽  
Zhen Huang ◽  
Hua F. Ding
Keyword(s):  
Kinematic Analysis ◽  
Jacobian Matrix ◽  
Hessian Matrix ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Analysis Method ◽  
Rear Part ◽  
Lower Mobility ◽  
Acceleration Analysis

This paper proposes a novel kinematic analysis method for a class of lower-mobility mechanisms whose degree-of-freedom (DoF) equal the number of single-DoF kinematic pairs in each kinematic limb if all multi-DoF kinematic pairs are substituted by the single one. For such an N-DoF (N<6) mechanism, this method can build a square (N×N) Jacobian matrix and cubic (N×N×N) Hessian matrix. The formulas in this method for different parallel mechanisms have unified forms and consequently the method is convenient for programming. The more complicated the mechanism is (for instance, the mechanism has more kinematic limbs or pairs), the more effective the method is. In the rear part of the paper, mechanisms 5-DoF 3-R(CRR) and 5-DoF 3-(RRR)(RR) are analyzed as examples.

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.

Reverse Kinematic Analysis of the Spatial Six Axis Robotic Manipulator With Consecutive Joint Axes Parallel

2007 ◽  
Author(s):  
Javier Rolda´n Mckinley ◽  
Carl Crane ◽  
David B. Dooner
Keyword(s):  
Kinematic Analysis ◽  
Closed Loop ◽  
Degree Of Freedom ◽  
Repetitive Motion ◽  
Spatial Mechanism ◽  
Joint Axis ◽  
Specific Geometry ◽  
Noncircular Gears ◽  
Six Degree Of Freedom ◽  
The Given

This paper introduces a reconfigurable one degree-of-freedom spatial mechanism that can be applied to repetitive motion tasks. The concept is to incorporate five pairs of noncircular gears into a six degree-of-freedom closed-loop spatial chain. The gear pairs are designed based on the given mechanism parameters and the user defined motion specification of a coupler link of the mechanism. It is shown in the paper that planar gear pairs can be used if the spatial closed-loop chain is comprised of six pairs of parallel joint axes, i.e. the first joint axis is parallel to the second, the third is parallel to the fourth, …, and the eleventh is parallel to the twelfth. This paper presents the detailed reverse kinematic analysis of this specific geometry. A numerical example is presented.

Geometric Design of a Bio-Inspired Flapping Wing Mechanism Based on Bennett-Derived 6R Deployable Mechanisms

2014 ◽  
Author(s):  
Huang Hailin ◽  
Li Bing
Keyword(s):  
Flapping Wing ◽  
Geometric Design ◽  
Geometric Parameters ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Flapping Motion ◽  
Single Degree ◽  
Revolute Joints ◽  
Air Vehicle ◽  
Deployable Mechanism

In this paper, we present the concept of designing flapping wing air vehicle by using the deployable mechanisms. A novel deployable 6R mechanism, with the deploying/folding motion of which similar to the flapping motion of the vehicle, is first designed by adding two revolute joints in the adjacent two links of the deployable Bennett linkage. The mobility of this mechanism is analyzed based on a coplanar 2-twist screw system. An intuitive projective approach for the geometric design of the 6R deployable mechanism is proposed by projecting the joint axes on the deployed plane. Then the geometric parameters of the deployable mechanism can be determined. By using another 4R deployable Bennett connector, the two 6R deployable wing mechanisms can be connected together such that the whole flapping wing mechanism has a single degree of freedom (DOF).

Kinematic Analysis and Simulation of the Translational Parallel Mechanism

2011 ◽  
Vol 213 ◽  
pp. 43-47 ◽  
Author(s):  
Dong Tao Xu ◽  
Zhi Li Sun ◽  
Jia Lian Shi
Keyword(s):  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Virtual Prototyping ◽  
Inverse Solution ◽  
Kinematic Modeling ◽  
Forward Solution ◽  
Vector Method ◽  
End Effector ◽  
Kinematic Simulation ◽  
Revolute Joints

This paper presents a novel, precision, maneuverable, 3-DOF translational parallel mechanism. The mechanism’s important feature is that all of the kinematic joints are the revolute joints. The paper derives the mechanism’s kinematic forward solution and inverse solution by using of coordinate transformation elimination method and vector method, and establishes proper kinematic modeling. Kinematic simulation is carried out by ADAMS virtual prototyping software. The operating data is obtained, it verifies the correctness of solving the forward and inverse solution, and solve the question of choices for many results during the theoretical solution. This technique can provide a useful tool in the design of kinematic trajectory of the parallel mechanism’s end-effector and the kinematic analysis of other parallel mechanism.

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