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.

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.

scholarly journals Instant Center Identification of Single-Loop Multi-DOF Planar Linkage Using Virtual Link

2021 ◽  
Vol 11 (10) ◽  
pp. 4463
Author(s):  
Liangyi Nie ◽  
Huafeng Ding ◽  
Kwun-Lon Ting ◽  
Andrés Kecskeméthy
Keyword(s):  
Singularity Analysis ◽  
Kinematic Characteristic ◽  
Virtual Link ◽  
Dynamics Modeling ◽  
Single Loop ◽  
Straightforward Method ◽  
Prismatic Joints ◽  
Configuration Synthesis ◽  
Definition Of ◽  
Planar Linkages

Instant center is an important kinematic characteristic which can be used for velocity and singularity analysis, configuration synthesis and dynamics modeling of multi-degree of freedom (multi-DOF) planar linkage. The Aronhold–Kennedy theorem is famous for locating instant centers of four-bar planar linkage, but for single-loop multi-DOF linkages, it fails. Increasing with the number of the links of single-loop multi-DOF planar linkages, the lack of link relationship makes the identification of instant center become a recognized difficulty. This paper proposes a virtual link method to identify instant centers of single-loop multi-DOF planar linkage. First, three types of instant centers are redefined and the instant center identification process graph is introduced. Then, based on coupled loop chain characteristic and definition of instant center, two criteria are presented to convert single-loop multi-DOF planar linkage into a two-loop virtual linkage by adding the virtual links. Subsequently, the unchanged instant centers are identified in the virtual linkage and used to acquire all the instant centers of original single-loop multi-DOF planar linkage. As a result, the instant centers of single-loop five-bar, six-bar planar linkage with several prismatic joints are systematically researched for the first time. Finally, the validity of the proposed method is demonstrated using loop equations. It is a graphical and straightforward method and the application is wide up to single-loop multi-DOF N-bar (N ≥ 5) planar linkage.

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.

Mass Flow and Derivative Moment of Inertia Flow in Planar (Geared) Linkages

1992 ◽  
Author(s):  
Zhonghe Ye ◽  
M. R. Smith
Keyword(s):  
Mass Flow ◽  
Kinematic Analysis ◽  
Moment Of Inertia ◽  
Force Balance ◽  
New Concepts ◽  
Prismatic Joints ◽  
Planar Linkages ◽  
First Time ◽  
Shaking Moment

Abstract The paper describes a method for the determination of the conditions for the complete shaking force and shaking moment balancing of planar linkages, including geared linkages, with revolute and prismatic joints. The conditions may be written down without the need for any kinematic analysis of the linkage by the application of two new concepts. These are the concept of mass flow for complete shaking force balance and the concept of derivative moment of inertia flow for complete shaking moment balance, the second of which is described here for the first time. A number of examples demonstrate the power of the method.

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 Computer Implementation of the Position Solution of Planar Linkages Using Vector Loop Decomposition

1998 ◽  
Author(s):  
Clint A. Kahler ◽  
J. Keith Nisbett ◽  
Clement R. Goodin
Keyword(s):  
Closed Form ◽  
Computer Software ◽  
Computer Implementation ◽  
Software Application ◽  
Prismatic Joints ◽  
Position Solution ◽  
Planar Linkages ◽  
Form Approach ◽  
Independent Loops

Abstract A general closed-form approach to the solution of loop equations of planar n-bar linkages is presented. Each loop of a set of canonical independent loops is decomposed to a set of vectors. Several common combinations of revolute and prismatic joints are defined. By evaluating the types of joints at each end of a vector, the magnitude and direction of the vector are determined to be known constants or unknown variables. This leads to an identification of the number of unknowns and the distribution of unknowns in the loop. This identification allows the unknowns to be found by matching the situation to one of the unique, closed-form cases for a solvable loop. A computer software application has been developed and is analyzed for efficiency.

Study of Torsion Spring’s Parameters with Angular Type Grippers

2012 ◽  
Vol 502 ◽  
pp. 355-359 ◽  
Author(s):  
Dong Hwan Shin ◽  
Tae Sang Park ◽  
Choong Pyo Jeong ◽  
Yoon Gu Kim ◽  
Ji Nung An
Keyword(s):  
Frictional Coefficient ◽  
Torsional Stiffness ◽  
Dynamics Simulation ◽  
Design Parameters ◽  
Active Joint ◽  
Linear Type ◽  
Passive Joint ◽  
Gravity Forces ◽  
Torsional Spring ◽  
Gripping Force

Angular type grippers are proper to grip the small size material than linear type grippers (clamping). It is due to the grip force of angular type grippers separates to the normal and the opposite directional force to gravity forces, when the contact between the gripper tip and the gripped material occurs. Whereas, the linear type gripper with prismatic joint has only normal forces. Therefore, even less gripping force of angular type grippers than linear type can generate slip-less pick-and-place motions. But this angular type gripper has some restrictions. For generating the opposite direction force to gravity forces, it is necessary that the length between each angular joint position is larger than the length of gripped materials. This should be considered on the design step of angular type grippers. Otherwise, the gripping force separates to the normal and the same directional force to gravity forces. The other restriction is that the tip of gripper must have passive joint or active joint for the plane-to-plane contact between faces of gripped material and gripper tip, for getting the high frictional coefficient. In this paper, we describe the case of adaptation of passive joint. This leads simpler implementation than the active joint. Especially, we focus on the torsional spring deposed at between jaw link and tip as the passive joint, with effects of design parameters of this torsional spring such as the torsional stiffness and preload with multi-body dynamics simulation.

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