Uncertainty of Coupler Point Position of Slider Crank Mechanisms

2015 ◽  
Author(s):  
Zetao Yu ◽  
Kwun-Lon Ting ◽  
Kuan-Lun Hsu ◽  
Jun Wang ◽  
Wesley Waggoner
Keyword(s):  
Geometric Model ◽  
Joint Clearance ◽  
Link Length ◽  
Position Uncertainty ◽  
Prismatic Joint ◽  
Point Position ◽  
Joint Clearances ◽  
Crank Mechanism ◽  
Short Link

In this paper, a novel geometric model for a planar slider-crank mechanism is established to quantify the position uncertainty of a coupler point caused by joint clearances. The clearance of each revolute and prismatic joint is characterized by a short clearance link. The prismatic joint with clearance is modeled as a link with infinite link length and a variable short link. The linkage with joint clearance is thus modeled as one with redundant freedom. The uncertainty is the result of the redundancy and the extremity of the redundancy is determined through Ting’ N-bar rotatability laws.

Joint Clearances With Lubricated Long Bearings in Multibody Mechanical Systems

1999 ◽  
Vol 122 (4) ◽  
pp. 484-488 ◽  
Author(s):  
P. Ravn ◽  
S. Shivaswamy ◽  
B. J. Alshaer ◽  
Hamid M. Lankarani
Keyword(s):  
Mechanical Systems ◽  
Steady Motion ◽  
Joint Clearance ◽  
Hydrodynamic Theory ◽  
Viscous Effects ◽  
Analysis And Design ◽  
Joint Clearances ◽  
The Impact ◽  
Crank Mechanism ◽  
Hydrodynamic Theory Of Lubrication

Proper modeling of joint clearance is of great importance in the analysis and design of multibody mechanical systems. The clearance may be due to wear or imperfection in manufacturing. When there is no lubricant in the clearance, solid-to-solid contact occurs. The impulse due to contact between the links is transmitted throughout the system. The presence of a lubricant avoids such contact, as the hydrodynamic forces developed by the lubricant film support the loads acting on the bodies and prevent the bodies from coming into contact. In this paper, an analysis of revolute joint clearances in multibody mechanical systems with and without lubricant is presented. Squeeze as well as viscous effects are considered utilizing the hydrodynamic theory of lubrication in long bearings. Unlike the traditional machine design approach, the instantaneous lubricant forces are the unknown and evaluated in terms of the known geometrical position and velocity of the journal and bearing. In the case of analysis of a joint clearance with no lubricant, a modified Hertzian relation is used to model the impact or contact between the journal and bearing, which includes a hysteresis damping term to account for the energy dissipation during impact. The methodology is applied for the analysis of a slider-crank mechanism having a clearance in the piston pin. The simulations are carried out with and without lubricant and the results are compared. It is shown that the lubricant results in a steady motion with fewer peaks in the required cranking moment for the system. [S1050-0472(00)01804-3]

Treatment of Lubrication in Long Bearings for Joint Clearances in Multibody Mechanical Systems

1999 ◽  
Author(s):  
P. Ravn ◽  
S. Shivaswamy ◽  
H. M. Lankarani
Keyword(s):  
Mechanical Systems ◽  
Steady Motion ◽  
Machine Design ◽  
Joint Clearance ◽  
Hydrodynamic Theory ◽  
Solid Contact ◽  
Damping Term ◽  
Joint Clearances ◽  
The Impact ◽  
Crank Mechanism

Abstract Proper modeling of joint clearance is of great importance in the analysis of multibody mechanical systems. The clearance may be due to wear or imperfection in manufacturing. When there is no lubricant in the clearance, solid-to-solid contact occurs. The impulse due to contact between the links is transmitted throughout the system. The presence of a lubricant avoids such contact, as the hydrodynamic forces developed by the lubricant film supports the loads acting on the bodies and prevents the bodies from coming into contact. In this paper, an analysis of revolute joint clearances in multibody mechanical systems with and without lubricant is presented. Hydrodynamic theory of long bearing is utilized in this study. Unlike the traditional machine design approach, the instantaneous lubricant forces are the unknown and evaluated in terms of the known geometrical position and velocity of the journal and bearing. In the case of analysis of a joint clearance with no lubricant, a modified Hertzian relation is used to model the impact or contact between the journal and bearing, which includes a hysteresis damping term to account for the energy dissipation during impact. The methodology is applied for the analysis of a slider-crank mechanism having a clearance in the piston pin. The simulations are carried out with and without lubricant and the results are compared. It is shown that the lubricant results in a steady motion with fewer peaks in the required cranking moment for the system.

Clearance-Induced Position Uncertainty of Planar Linkages and Parallel Manipulators

2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Kwun-Lon Ting ◽  
Kuan-Lun Hsu ◽  
Jun Wang
Keyword(s):  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Target Position ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Joint Clearance ◽  
Position Uncertainty ◽  
Kinematic Effect ◽  
Joint Clearances

The paper presents a simple and effective kinematic model and methodology to assess and evaluate the extent of the position uncertainty caused by joint clearances for multiple-loop 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 contributions include (1) the clearance link model for a P-joint that catches the translation and oscillation characteristics of the slider within the clearance and separates the geometric effect of clearances from the input error, (2) the generality of the method, which is effective for multiloop linkages and parallel manipulators, and (3) settling the dispute on the position uncertainty effect to parallel and serial robots due to joint clearance. The discussion is illustrated and carried out through symmetrically configured planar 8 bar parallel robots. It is found that at a target position, the uncertainty region of a three degrees-of-freedom (DOF) three-leg parallel robot is enclosed by a hexagon with curve edges, while that of its serial counterpart is enclosed by a circle included in the hexagon. A numerical example is 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 the kinematic effect of joint clearance, parallel robots tends to inherit more position uncertainty than their serial counterparts. The use of more loops in not only parallel robots but also single-DOF linkages cannot fully offset the adverse effect on position uncertainty caused by the use of more joints.

Tolerance Analysis of a Robot Manipulator Having Uncertainties in Joint Clearance and Axis Orientation

2007 ◽  
Author(s):  
Dong Hwan Choi ◽  
Se Jeong Lee ◽  
Jonathan A. Wickert ◽  
Hong Hee Yoo
Keyword(s):  
Robot Manipulator ◽  
Statistical Design ◽  
Tolerance Analysis ◽  
Joint Clearance ◽  
Design Parameters ◽  
Positional Error ◽  
Link Length ◽  
Axis Orientation ◽  
Manufacturing Tolerances ◽  
Clearance Model

The operating positional error of a robot manipulator, which develops inevitably because of manufacturing tolerances and assembly clearances, is preferentially maintained within a certain range in order to achieve an acceptable level of performance and accuracy. Because additional cost is incurred when manufacturing tolerances are tightened, an alternative design strategy maximizes the tolerances (so as to reduce the cost) while minimizing positioning error (to satisfy a performance requirement). In this paper, a new joint clearance model is developed for spatial mechanisms that incorporate revolute joints, which in turn are subjected to specified tolerance or uncertainty in the orientation of their axes. Statistical design parameters related to variations of link length and joint axis orientation are identified from the clearance model. The statistical influence of the design parameters on the robot manipulator’s response is investigated through a general multibody dynamics sensitivity formulation. The method offers substantial improvement in computational efficiency when compared to the Monte Carlo procedure. The uncertainty in orientation of a revolute joint’s axis influences the positioning accuracy of the robot manipulator’s response to a greater degree than does uncertainty in the length of a link.

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).

Accuracy analysis and optimization of an extendible support structure with joint clearances

2020 ◽  
pp. 095440622097305
Author(s):  
Jianzhong Ding ◽  
Chunjie Wang
Keyword(s):  
Monte Carlo ◽  
Reduction Method ◽  
Global Sensitivity Analysis ◽  
Angular Error ◽  
Joint Clearance ◽  
Design Parameters ◽  
Support Structure ◽  
Quasi Monte Carlo ◽  
Joint Clearances ◽  
Independent Parameters

An extendible support structure (ESS) used for unfolding and supporting the antenna array of the Synthetic Aperture Radar (SAR) satellite is reviewed and modeled in this paper. The structure is parameterized by calibrating 12 independent parameters, and following which, angular accuracy of the ESS with joint clearances is modeled. The maximum angular error is obtained by the particle swarm optimization (PSO) and validated by the Monte Carlo simulation. A novel error reduction method is then proposed to improve the accuracy of the structure. In the proposed method, the uncertainty of the joint clearance is eliminated using force constraints by adding small torsional springs. Various joint clearance models with force constraints are proposed to obtain the optimal spring allocation, and based on which, the angular error is further reduced by optimizing the structure of the ESS. The Quasi-Monte-Carlo-based Sobol method for global sensitivity analysis is used to select the design parameters for optimization. Finally, the angular error is greatly reduced.

Identifying joint clearance via robot manipulation

2017 ◽  
Vol 232 (15) ◽  
pp. 2549-2574 ◽  
Author(s):  
Kuan-Lin Li ◽  
Ying-Kuan Tsai ◽  
Kuei-Yuan Chan
Keyword(s):  
Robot Manipulators ◽  
Optimal Path ◽  
Optimal Operation ◽  
Joint Clearance ◽  
Average Error ◽  
Robot Manipulation ◽  
Uncertainty Sources ◽  
Time Calibration ◽  
Joint Clearances ◽  
Improved Accuracy

Inaccuracy in robot manipulation is a result of various uncertainties. Most methods reduce operation errors by calibrating robot parameters, with little attention on understanding the uncertainty sources in the process. This paper investigates how operation accuracy of robot manipulators can be improved by identifying one of the major uncertainty–joint clearance. We first develop the dynamic model of a Delta robot with joint clearance to obtain the operation error of a given trajectory. Errors with different operating procedures can, therefore, be calculated. We then use a Kriging-based model to relate manipulator performances with joint clearance values. Real-time calibration can then be performed by identifying joint clearance via experiments. Errors can also be reduced using optimal path planning with the calibrated joint clearance. Results show that this method reduces the average error at target points from 0.637 to 0.031 mm for robot manipulators with joint clearances of 0.328, 0.171, and 0.483 mm. This is a 95.1% improvement in accuracy over that for the manipulator before optimization. The proposed method can help manufacturers determine robot quality, and achieve optimal operation in a workspace with improved accuracy.

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