On the Mobility of Single Loop N-Bar Linkage With One Prismatic Joint

2005 ◽  
Author(s):  
W. Z. Guo ◽  
R. Du ◽  
J. X. Wang
Keyword(s):  
Change Point ◽  
Open Loop ◽  
Class Iii ◽  
Revolute Joint ◽  
Single Loop ◽  
Prismatic Joint ◽  
Revolute Joints ◽  
Offset Distance ◽  
Special Cases ◽  
Prismatic Joints

Single loop N-bar linkages that contain one prismatic joint are common in engineering. This paper presents a systematical study on the mobility of this type of mechanism. It is found that this type of mechanisms can be divided into three categories: Class I, Class II and Class III. For each category, the slide reachable range is cut into different regions: Grashofian region, non-Grashofian region and change-point region. At each region, the rotation range of the revolute joint or rotatability of the linkage is able to determine based on Ting’s criteria. The characteristics charts are given to describe the rotatability condition. For active prismatic joint, the input revolute joint(s) is/are dependent in non-Grashofian region but independent in other regions. For passive prismatic joint, the revolvability of input revolute joints is dependent on the offset distance of the prismatic joint. Two special cases are illustrated with four and five bars. Examples are given to demonstrate the presented method able to cover all the cases of N-bar linkages with one or a set of adjoined prismatic joints and N-bar open-loop robotic mechanisms.

Mobility of Single-Loop N-Bar Linkage With Active/Passive Prismatic Joints

2005 ◽  
Vol 128 (6) ◽  
pp. 1261-1271 ◽  
Author(s):  
W. Z. Guo ◽  
R. Du
Keyword(s):  
Open Loop ◽  
Class Iii ◽  
Active Joint ◽  
Revolute Joint ◽  
Single Loop ◽  
Prismatic Joint ◽  
Passive Joint ◽  
Offset Distance ◽  
Prismatic Joints ◽  
Planar Linkages

Single-loop N-bar linkages that contain one prismatic joint are common in engineering. This type of mechanism often requires complicated control and, hence, understanding its mobility is very important. This paper presents a systematic study on the mobility of this type of mechanism by introducing the concept of virtual link. It is found that this type of mechanism can be divided into three categories: Class I, Class II, and Class III. For each category, the slide reachable range is cut into different regions: Grashof region, non-Grashof region, and change-point region. In each region, the rotation range of the revolute joint or rotatability of the linkage can be determined based on Ting’s criteria. The characteristics charts are given to describe the rotatability condition. Furthermore, if the prismatic joint is an active joint, the revolvability of the input revolute joint is dependent in non-Grashof region but independent in other regions. If the prismatic joint is a passive joint, the revolvability of the input revolute joint is dependent on the offset distance of the prismatic joint. Two examples are given to demonstrate the presented method. The new method is able to cover all the cases of N-bar planar linkages with one or a set of adjoined prismatic joints. It can also be used to study N-bar open-loop planar robotic mechanisms.

Mobility Criteria of Planar Single-Loop N-Bar Chains With Prismatic Joints

2011 ◽  
Vol 3 (1) ◽  
Author(s):  
Changyu Xue ◽  
Kwun-Lon Ting ◽  
Jun Wang
Keyword(s):  
Revolute Joint ◽  
Single Loop ◽  
Prismatic Joint ◽  
Prismatic Joints ◽  
Consistent Method

This paper presents the extension of the N-bar rotatability laws to N-bar chains containing prismatic joints. The extension is based on the principle that a prismatic joint may be regarded as a revolute joint located at infinity in the direction normal to the sliding path. The effects of long and short links, full rotatability, linkage classification, and formation of branches and sub-branches are discussed. The extension provides a consistent method to understand all aspects of linkage rotatability disregarding the existence of prismatic joints. The results are demonstrated by several examples.

Mobility Criteria of Planar Single-Loop N-Bar Chains With Prismatic Joints

2008 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Changyu Xue ◽  
Jun Wang ◽  
Kenneth R. Currie
Keyword(s):  
Revolute Joint ◽  
Single Loop ◽  
Prismatic Joint ◽  
Prismatic Joints ◽  
Consistent Method

The paper offers an extension of Ting’s rotatability laws to N-bar chains connected by revolute and prismatic joints. The extension is based on the principle that a prismatic joint may be regarded as a revolute joint located at infinity in the direction normal to the path of the slider. The extension provides a consistent method to understand all aspects of linkage rotatability disregarding the existence of prismatic joints. The simplicity and consistency of its applications is demonstrated with examples.

A non-overconstrained variant of the Agile Eye with a special decoupled kinematics

Robotica ◽  
2013 ◽  
Vol 32 (6) ◽  
pp. 889-905 ◽  
Author(s):  
Chin-Hsing Kuo ◽  
Jian S. Dai ◽  
Giovanni Legnani
Keyword(s):  
Angular Displacement ◽  
Universal Joint ◽  
Special Configuration ◽  
End Effector ◽  
Revolute Joint ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Decoupled Motion ◽  
Orientation Mechanism ◽  
Actuated Joints

SUMMARYA non-overconstrained three-DOF parallel orientation mechanism that is kinematically equivalent to the Agile Eye is presented in this paper. The output link (end-effector) of the mechanism is connected to the base by one spherical joint and by another three identical legs. Each leg comprises of, in turns from base, a revolute joint, a universal joint, and three prismatic joints. The three lower revolute joints are active joints, while all other joints are passive ones. Based on a special configuration, some three projective angles of the end-effector coordinates are fully decoupled with respect to the input actuated joints, that is, by actuating any revolute joint the end-effector rotates in such a way that the corresponding projective angle changes with the same angular displacement. The fully decoupled motion is analyzed geometrically and proved theoretically. Besides, the inverse and direct kinematics solutions of the mechanism are provided based on the geometric reasoning and theoretical proof.

Graphical Methods to Locate the Secondary Instant Centers of Single-Degree-of-Freedom Indeterminate Linkages

2005 ◽  
Vol 127 (2) ◽  
pp. 249-256 ◽  
Author(s):  
David E. Foster ◽  
Gordon R. Pennock
Keyword(s):  
Degree Of Freedom ◽  
Graphical Methods ◽  
Single Degree Of Freedom ◽  
Revolute Joint ◽  
Single Degree ◽  
Revolute Joints ◽  
Straight Line ◽  
Single Link ◽  
Prismatic Joints ◽  
Two Degree Of Freedom

This paper presents graphical techniques to locate the unknown instantaneous centers of zero velocity of planar, single-degree-of-freedom, linkages with kinematic indeterminacy. The approach is to convert a single-degree-of-freedom indeterminate linkage into a two-degree-of-freedom linkage. Two methods are presented to perform this conversion. The first method is to remove a binary link and the second method is to replace a single link with a pair of links connected by a revolute joint. First, the paper shows that a secondary instant center of a two-degree-of-freedom linkage must lie on a unique straight line. Then this property is used to locate a secondary instant center of the single-degree-of-freedom indeterminate linkage at the intersection of two lines. The two lines are obtained from a purely graphical procedure. The graphical techniques presented in this paper are illustrated by three examples of single-degree-of-freedom linkages with kinematic indeterminacy. The examples are a ten-bar linkage with only revolute joints, the single flier eight-bar linkage, and a ten-bar linkage with revolute and prismatic joints.

scholarly journals Spatial Straight-Line Linkages by Factorization of Motion Polynomials

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Zijia Li ◽  
Josef Schicho ◽  
Hans-Peter Schröcker
Keyword(s):  
End Effector ◽  
Single Loop ◽  
Revolute Joints ◽  
Straight Line ◽  
Prismatic Joints ◽  
Spatial Linkages ◽  
Line Trajectory ◽  
Straight Line Trajectory

We use the recently introduced factorization of motion polynomials for constructing overconstrained spatial linkages with a straight-line trajectory. Unlike previous examples of such linkages by other authors, they are single-loop linkages and the end-effector motion is not translational. In particular, we obtain a number of linkages with four revolute and two prismatic joints and a remarkable linkage with seven revolute joints one of whose joints performs a Darboux motion.

scholarly journals Synthesis and static analysis of the deployable frame for a morphing wing

2012 ◽  
Vol 227 (3) ◽  
pp. 565-579 ◽  
Author(s):  
Jing-Shan Zhao ◽  
Li Ye ◽  
Fulei Chu ◽  
Jian S Dai
Keyword(s):  
Numerical Analysis ◽  
Static Analysis ◽  
Structural Stiffness ◽  
Morphing Wing ◽  
Folding Process ◽  
Prismatic Joint ◽  
Structure And Motion ◽  
Revolute Joints ◽  
Primary Element ◽  
Prismatic Joints

This article proposes a deployable frame for a morphing wing. The frame is redundantly constrained in structure, and therefore it has both merits of high structural stiffness and strength of a truss structure and motion flexibility of a mechanism. The primary element of the foldable frame is synthesized from the viewpoint of identical strength principle. The major structures of previous deployable wings are mostly based on prismatic joints. However, the deflections of the cantilevered links might not satisfy the primary geometry requirements of the prismatic joint. Therefore revolute joints are used in our deployable frame to avoid violating the geometry conditions for prismatic joints resulting from the different deflections of its contacting two parts. The deflection and slope of every joint node of the foldable frame is investigated within the deploying/folding process. Numerical analysis indicates that the deployment ratio of the foldable frame can be designed much larger than that of the existing morphing wing even considering the allowable deflection under the completely unfolded situations.

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.

Analysis and Synthesis of Linear Transmission Mechanisms: Coupled Mechanisms and Mechanisms Wth Prismatic Joints

1994 ◽  
Author(s):  
Sun-Lai Chang
Keyword(s):  
Open Loop ◽  
Joint Motion ◽  
Transmission Mechanisms ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis ◽  
Prismatic Joints ◽  
Application Potential ◽  
Loop Chain

Abstract The characteristics of linear transmission mechanisms are studied. Using the characteristics, the kinematic and synthesis of linear transmission mechanisms are expanded. First, the synthesis of mechanisms with prismatic joints in the equivalent open-loop chain is developed. Then the kinematics and synthesis of mechanisms with coupled joint motion are also derived. Two coupled mechanisms are used as examples to demonstrate the application potential in the industry.

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.

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