scholarly journals Assembly conditions of parallel manipulators considering geometric errors, joint clearances, link flexibility and joint elasticity

2014 ◽  
Author(s):  
Davide Corradi ◽  
Stephane Caro ◽  
Damien Chablat ◽  
Philippe Cardou
Keyword(s):  
Parallel Manipulators ◽  
Geometric Errors ◽  
Joint Elasticity ◽  
Link Flexibility ◽  
Joint Clearances

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).

Motion Reliability Analysis of a 3-RRR Parallel Manipulator With Random and Interval Variables

2016 ◽  
Author(s):  
Zhenhui Zhan ◽  
Xianmin Zhang
Keyword(s):  
Reliability Analysis ◽  
Parallel Manipulator ◽  
Random Variable ◽  
Parallel Manipulators ◽  
Analysis Method ◽  
Motion Error ◽  
Interval Variables ◽  
First Order Second Moment ◽  
Joint Clearances ◽  
Mcs Method

A general methodology for motion error and motion reliability analysis of planar parallel manipulators (PPMs) with random and interval variables is presented. The inherent uncertainties of the manipulator, including tolerances in manufactures, errors in inputs as well as joint clearances are taken into account. The error model of a 3-RRR parallel manipulator is built and the global sensitivity coefficients of motion errors to variations are defined and obtained. The joint clearances are treated as interval variables while the others are treated as random variables. As a result, the motion error of the manipulator could turn out to be the mixture of a random variable and an interval variable. A new motion reliability analysis method based on the First Order Second Moment (FOSM) method and the Monte Carlo simulation (MCS) method is developed for the manipulator with random and interval variables. This paper provides a new idea to better understand the motion reliability affected by the inherent uncertainties of PPMs.

Application of Workspace Generation Techniques to Determine the Unconstrained Motion of Parallel Manipulators

2004 ◽  
Vol 126 (2) ◽  
pp. 283-290 ◽  
Author(s):  
Philip Voglewede ◽  
Imme Ebert-Uphoff
Keyword(s):  
Large Class ◽  
General Framework ◽  
Parallel Manipulators ◽  
End Effector ◽  
Singular Configurations ◽  
Joint Clearances ◽  
Generation Problem ◽  
Unconstrained Motion

Due to clearances in their passive joints, parallel manipulators always exhibit some unconstrained motion at the end effector. The amount of unconstrained motion depends on the pose of the manipulator and can increase significantly at or near singular configurations. This paper shows precisely how much unconstrained end effector motion exists at the end effector for a large class of parallel manipulators, namely those with passive revolute and/or spherical joints, if all the joint clearances are known. This includes the planar 3R_RR, and, in approximation the Gough-Stewart and the Hexa manipulators. For the analysis, the passive joints are assumed to be revolute or spherical because these are the simplest cases. However, the general framework also applies to other joint types, although leading to more complex calculations. For most manipulators, determining the amount of end effector motion can be transformed to a workspace generation problem. Therefore, general workspace generation techniques can be utilized.

scholarly journals The Kinematic Sensitivity of Robotic Manipulators to Joint Clearances

2010 ◽  
Author(s):  
Nicolas Binaud ◽  
Philippe Cardou ◽  
Ste´phane Caro ◽  
Philippe Wenger
Keyword(s):  
Reference Point ◽  
Robotic Manipulators ◽  
Parallel Manipulators ◽  
Error Prediction ◽  
Orientation Error ◽  
Moving Platform ◽  
Joint Clearances ◽  
Kinematic Sensitivity ◽  
Quadratically Constrained ◽  
Clearance Model

The paper deals with the kinematic sensitivity of robotic manipulators to joint clearances. First, an error prediction model applicable to both serial and parallel manipulators is developed. A clearance model associated with axisymmetrical joints, which are widely used in robotic manipulators, is also proposed. Then, two nonconvex quadratically constrained quadratic programs (QCQPs) are formulated in order to find the maximum reference-point position error and the maximum orientation error of the moving-platform for given joint clearances. Finally, the contributions of the paper are highlighted by means of two illustrative examples.

Formulation and control of robots with link and joint flexibility

Robotica ◽  
1993 ◽  
Vol 11 (3) ◽  
pp. 273-282 ◽  
Author(s):  
Sachin Gogate ◽  
Yueh-Jaw Lin
Keyword(s):  
Effective Control ◽  
Nonlinear Feedback ◽  
Joint Flexibility ◽  
Vibration Model ◽  
Modes Of Vibration ◽  
Manipulator Link ◽  
Joint Elasticity ◽  
Simultaneous Existence ◽  
Link Flexibility ◽  
And Control

SUMMARYPresent study on industrial manipulator control either completely neglects structural flexibility or only considers manipulator link flexibility. Ignoring joint flexibility may cause significant errors in gross motion control if the joint elastic effect is predominant. This paper presents an effective control scheme which can compensate for the motion errors generated by simultaneous existence of both link and joint flexibility. The manipulator dynamics is formulated comprehensively by a superposition of two models, namely, an assumed modes of vibration model for links and a torsional spring model.for joints. Then, a nonlinear feedback rate servo control system is developed that compensates for the gross motion errors introduced by both joint elasticity and link flexibility. Motion simulation results show that the proposed formulation can effectively describe the dynamic behavior of a flexible-link, elastic-joint robot. They also verify that the proposed controller is robust in that it can satisfactorily suppress the manipulator end oscillations and yield an accurate gross motion.

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