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.

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 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.

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.

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.

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.

Assembly Configurations of Spatial Single-Loop Mechanisms With Revolute, Cylindric, and Prismatic Joints

1998 ◽  
Author(s):  
David E. Foster ◽  
Raymond J. Cipra
Keyword(s):  
Single Loop ◽  
Spatial Mechanisms ◽  
Prismatic Joints ◽  
Spherical Mechanism

Abstract This paper examines the problem of identifying the assembly configurations (ACs), also called circuits, of certain spatial single-loop mechanisms. First, the spherical mechanism is considered; it is believed that such a mechanism has one AC if every pair of adjacent links can line up; otherwise, it has 2 ACs. Next, general spatial mechanisms with revolute, cylindric, and prismatic points are considered. If the mechanism has three or more sliding (cylindric or prismatic) joints, it is possible to find an equivalent spherical mechanism which has the same angular motions. However, it is also possible that at certain positions, some of the links may have to slide an infinite distance, which is not possible. Therefore, the mechanism may have more ACs than the equivalent spherical mechanism. Several examples are given, and some general conclusions are drawn.

Compositional Submanifolds of Prismatic–Universal–Prismatic and Skewed Prismatic–Revolute– Prismatic Kinematic Chains and Their Derived Parallel Mechanisms

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Xinsheng Zhang ◽  
Pablo López-Custodio ◽  
Jian S. Dai
Keyword(s):  
Parallel Mechanism ◽  
Kinematic Chain ◽  
Planar Motion ◽  
Helical Motion ◽  
Parallel Mechanisms ◽  
Motion Group ◽  
Revolute Joint ◽  
Kinematic Chains ◽  
Prismatic Joint ◽  
Joint Axis

The kinematic chains that generate the planar motion group in which the prismatic-joint direction is always perpendicular to the revolute-joint axis have shown their effectiveness in type synthesis and mechanism analysis in parallel mechanisms. This paper extends the standard prismatic–revolute–prismatic (PRP) kinematic chain generating the planar motion group to a relatively generic case, in which one of the prismatic joint-directions is not necessarily perpendicular to the revolute-joint axis, leading to the discovery of a pseudo-helical motion with a variable pitch in a kinematic chain. The displacement of such a PRP chain generates a submanifold of the Schoenflies motion subgroup. This paper investigates for the first time this type of motion that is the variable-pitched pseudo-planar motion described by the above submanifold. Following the extraction of a helical motion from this skewed PRP kinematic chain, this paper investigates the bifurcated motion in a 3-prismatic–universal–prismatic (PUP) parallel mechanism by changing the active geometrical constraint in its configuration space. The method used in this contribution simplifies the analysis of such a parallel mechanism without resorting to an in-depth geometrical analysis and screw theory. Further, a parallel platform which can generate this skewed PRP type of motion is presented. An experimental test setup is based on a three-dimensional (3D) printed prototype of the 3-PUP parallel mechanism to detect the variable-pitched translation of the helical motion.

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.

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