Clearance-induced output position uncertainty of planar linkages with revolute and prismatic joints

2017 ◽  
Vol 111 ◽  
pp. 66-75 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Kuan-Lun Hsu ◽  
Zetao Yu ◽  
Jun Wang
Keyword(s):  
Position Uncertainty ◽  
Output Position ◽  
Prismatic Joints ◽  
Planar Linkages

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.

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.

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.

Clearance-Induced Position Uncertainty of Planar Linkages and Parallel Manipulators

2017 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Kuan-Lun Hsu
Keyword(s):  
Kinematic Model ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Position Uncertainty ◽  
Joint Clearances ◽  
Planar Linkages ◽  
Oscillation Characteristics ◽  
Linkage Model ◽  
Input Error

The paper presents a simple and effective kinematic model and methodology, based on Ting’s N-bar rotatability laws [2629], to assess the extent of the position uncertainty caused by joint clearances for any linkage and manipulators connected with revolute or prismatic pairs. The model is derived and explained with geometric rigor based on Ting’s rotatability laws. The significant contribution includes (1) the clearance link model for P-joint that catches the translation and oscillation characteristics of the slider within the clearance and separates the geometric effect of clearance from the input error, (2) a simple uncertainty linkage model that features a deterministic instantaneous structure mounted on non-deterministic flexible legs, (3) the generality of the method, which is effective for multiloop linkages and parallel manipulators. The discussion is carried out through symmetrically constructed planar eight-bar parallel robots. It is found that the uncertainty region of a three-leg parallel robot is enclosed by a hexagon, while that of its serial counterpart is enclosed by a circle inscribed by the hexagon. A numerical example is also presented. The finding and proof, though only based on three-leg planar 8-bar parallel robots, may have a wider implication suggesting that based on kinematics, parallel robots tends to inherit more position uncertainty than their serial counterparts. The use of more loops in parallel robots cannot fully offset the adverse effect on position uncertainty caused by the use of more joints.

Rotatability of the Floating Link on Multi-Loop Planar Linkages

2020 ◽  
Vol 12 (6) ◽  
Author(s):  
Cody Leeheng Chan ◽  
Kwun-Lon Ting
Keyword(s):  
Rotation Angle ◽  
Parallel Manipulators ◽  
Orientation Error ◽  
Joint Rotation ◽  
Position Uncertainty ◽  
End Effector ◽  
Uncertainty Model ◽  
Branch Formation ◽  
Joint Clearances ◽  
Planar Linkages

Abstract This paper proposes a method to deal with the orientation uncertainty problem affected by joint clearances. To solve this problem, it is necessary to establish the theory of mobility of the floating link of multi-loop linkages. Since the theory of the mobility of floating link is yet complete, this paper provides a simple treatment to determine the rotatability between any two links, adjoined or not, in planar multi-loop linkages. The rotation angle of the floating link with respect to the reference link is defined so that there is no ambiguity in analyzing the rotation range of the floating link. Based on the joint rotation space (JRS) method, one may identify not only the branch formation but also the rotatability between any two links on each of the branches. It is a visualized method that reveals the rotation characteristic of multi-loop linkages. This paper demonstrates the rotation range of the floating link with respect to the reference link on six-bar Stephenson linkages, 2-degree-of-freedom (DOF). 7-bar linkages, and 3-DOF. Eight-bar parallel manipulators. This might be the first paper to deal with the rotatability of 3-DOF planar multi-loop linkages. This paper uses the method to predict the clearance-induced angle uncertainty of the 8-bar parallel manipulators, which determines the worst orientation error of the end-effector and fills up the void of the joint clearance uncertainty model proposed by Ting et al. (2017, “Clearance-Induced Position Uncertainty of Planar Linkages and Parallel Manipulators,” J. Mech. Rob., 9, p. 061001).

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.

Singularity Traces of Single Degree-of-Freedom Planar Linkages That Include Prismatic and Revolute Joints

2016 ◽  
Vol 8 (5) ◽  
Author(s):  
Saleh M. Almestiri ◽  
Andrew P. Murray ◽  
David H. Myszka ◽  
Charles W. Wampler
Keyword(s):  
Design Parameter ◽  
Closed Loop ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Motion Characteristics ◽  
Planar Linkages ◽  
General Method

This paper extends the general method to construct a singularity trace for single degree-of-freedom (DOF), closed-loop linkages to include prismatic along with revolute joints. The singularity trace has been introduced in the literature as a plot that reveals the gross motion characteristics of a linkage relative to a designated input joint and a design parameter. The motion characteristics identified on the plot include a number of possible geometric inversions (GIs), circuits, and singularities at any given value for the input link and the design parameter. An inverted slider–crank and an Assur IV/3 linkage are utilized to illustrate the adaptation of the general method to include prismatic joints.

Singularity Traces of Planar Linkages That Include Prismatic and Revolute Joints

2015 ◽  
Author(s):  
Saleh M. Almestiri ◽  
David H. Myszka ◽  
Andrew P. Murray ◽  
Charles W. Wampler
Keyword(s):  
Shape Change ◽  
Rigid Bodies ◽  
Closed Curves ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Kinematic Position ◽  
Motion Characteristics ◽  
Forward Kinematic ◽  
Planar Linkages ◽  
General Method

This paper presents a general method to construct a singularity trace for single degree-of-freedom, closed-loop linkages that include prismatic, in addition to, revolute joints. The singularity trace has been introduced in the literature as a plot that reveals the gross motion characteristics of a linkage relative to a designated input joint and design parameter. Previously, singularity traces were restricted to mechanisms composed of only rigid bodies and revolute joints. The motion characteristics identified on the plot include changes in the number of solutions to the forward kinematic position analysis (geometric inversions), singularities, and changes in the number of branches. To illustrate the adaptation of the general method to include prismatic joints, basic slider-crank and inverted slider-crank linkages are explored. Singularity traces are then constructed for more complex Assur IV/3 linkages containing multiple prismatic joints. These Assur linkages are of interest as they form an architecture that is commonly used for mechanisms capable of approximating a shape change defined by a general set of closed curves.

A Procedure for Force-Balancing Planar Linkages Using Counterweights

1978 ◽  
Vol 20 (4) ◽  
pp. 177-182 ◽  
Author(s):  
K. Oldham ◽  
M. J. Walker
Keyword(s):  
Equations Of Motion ◽  
Force Balance ◽  
Prismatic Joints ◽  
Minimum Number ◽  
Full Force ◽  
Planar Linkages

This paper presents a procedure for obtaining the conditions for a full force-balance of a planar linkage. It includes a check on whether a full force-balance is possible where the presence of prismatic joints or links that cannot be counter-weighted for some reason may preclude this. The procedure automatically uses the minimum number of counterweights and keeps the added inertia low. An example demonstrates the advantages of the procedure over those methods that require the derivation of the kinematic equations of motion for the linkage.

Output Position of Veridical and False Memories for Words

2004 ◽  
Author(s):  
Terrence M. Barnhardt ◽  
Hyun Choi ◽  
David R. Gerkens ◽  
Barbara Corbisier ◽  
Steven M. Smith
Keyword(s):  
False Memories ◽  
Output Position
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