Clearance-induced orientation uncertainty of spherical linkages

2021 ◽  
pp. 1-9
Author(s):  
Cody Chan ◽  
Kwun-Lon Ting
Keyword(s):  
Closed Loop ◽  
Kinematic Model ◽  
Parallel Manipulators ◽  
Open Loop ◽  
Joint Clearance ◽  
Worst Case ◽  
End Effector ◽  
Uncertainty Range ◽  
Uncertainty Region ◽  
Spherical Linkages

Abstract This paper proposes a kinematic model to evaluate the orientation uncertainty range of spherical linkages caused by the joint clearances. Based on the concepts of imaginary clearance link, spherical N-bar rotatability laws, and the invariant link rotatability, the uncertainty of the output angle can be treated as a mobility problem. And the uncertainty region of the end-effector is treated as a workspace problem for the remodeled linkage. The paper highlights the orientation error by isolating the kinematic effects of joint clearance from other error factors. The discussion is carried out through spherical four-bar linkages and five-bar linkages. Numeric examples are presented to demonstrate the uncertainty range of the output angle and the uncertainty region of the end-effector. The result shows that, in the worst case, the error of each joint clearance will be magnified in a closed-loop structure compared with linearly adding all the clearance error. This implies that from a kinematics point of view, closed-loop spherical linkages or parallel manipulators will lead to a greater deviation on the end-effector than its open-loop counterpart. Using more passive joints in the manipulator may result in more error possibilities.

Effect of Link Tolerance and Joint Clearance on End-Effector Positioning of the 3-PSP Manipulator Using Taguchi Method

2015 ◽  
Vol 798 ◽  
pp. 20-24 ◽  
Author(s):  
Fattah Hanafi Sheikhha ◽  
Alireza Akbarzadeh
Keyword(s):  
Taguchi Method ◽  
Parallel Manipulators ◽  
Open Loop ◽  
Joint Clearance ◽  
Kinematic Parameters ◽  
Positioning Accuracy ◽  
End Effector ◽  
Dimensional Tolerance ◽  
Random Nature ◽  
Kinematics Parameters

The use of parallel manipulators in industrial is growing. Among key advantages of parallel manipulators versus their serial counterparts, is their improved end-effector positioning accuracy than open-loop mechanism. However, undesirable dimensional tolerance and joint clearance can decrease the positioning accuracy of the end-effector. In this article, Taguchi method is applied to a 3-PSP parallel manipulator to determine how dimensional tolerance and joint clearance affects the accuracy of its end effector. Because of random nature of dimensional tolerance, it is assumed that actual value of all kinematic parameters are normally distributed. Taguchi method is then used and effect of tolerance on accuracy for each of the manipulator kinematics parameters is obtained. Finally, a tolerance set resulting in best accuracy is predicted by the Taguchi method. This tolerance is verified with a new set of experiment.

Modeling and control of new model in a spatial coordinates -3D- for cable-based robots

2015 ◽  
Vol 12 (2) ◽  
pp. 189-200 ◽  
Author(s):  
Fouad Inel ◽  
Billel Bouchmal ◽  
Lakhdar Khochmane
Keyword(s):  
Closed Loop ◽  
Geometric Model ◽  
Kinematic Model ◽  
End Effector ◽  
Modeling And Control ◽  
New Model ◽  
Spiral Trajectory ◽  
Spatial Coordinates ◽  
Point To Point ◽  
And Control

This paper presents a modeling and control of new model in a spatial coordinates (x, y, z), from this structures we choose: regular pyramid of a square basis manipulated by five cables and eight cables for a cubic shape. The main objective of this work is to integrate the axe (z) on the horizontal plane (x, y) i-e the plan 3D. This last their intervention especially when we obliged to transfer the end effector from point to point, for that we used the direct and inverse geometric model to study and simulate the end effector position of the robot with five and eight cables. A graphical user interface has been implemented in order to visualizing the position of the robot. Secondly, we present the desired path and determination the tensions and cables lengths of kinematic model required to follow spiral trajectory. At the end, we study the response of our systems in closed loop with a Proportional-Integrated-Derivative (PID) using MATLAB/Simulink which used to verify the performance of the controller.

Deployable Prismatic Structures With Rigid Origami Patterns

2016 ◽  
Vol 8 (3) ◽  
Author(s):  
Sicong Liu ◽  
Weilin Lv ◽  
Yan Chen ◽  
Guoxing Lu
Keyword(s):  
Closed Loop ◽  
Design Method ◽  
Kinematic Model ◽  
Deployable Structures ◽  
Engineering Applications ◽  
Single Degree Of Freedom ◽  
General Design ◽  
Plane Symmetric ◽  
Single Degree ◽  
Spherical Linkages

Rigid origami inspires new design technology in deployable structures with large deployable ratio due to the property of flat foldability. In this paper, we present a general kinematic model of rigid origami pattern and obtain a family of deployable prismatic structures. Basically, a four-crease vertex rigid origami pattern can be presented as a spherical 4R linkage, and the multivertex patterns are the assemblies of spherical linkages. Thus, this prismatic origami structure is modeled as a closed loop of spherical 4R linkages, which includes all the possible prismatic deployable structures consisting of quadrilateral facets and four-crease vertices. By solving the compatibility of the kinematic model, a new group of 2n-sided deployable prismatic structures with plane symmetric intersections is derived with multilayer, straight and curvy variations. The general design method for the 2n-sided multilayer deployable prismatic structures is proposed. All the deployable structures constructed with this method have single degree-of-freedom (DOF), can be deployed and folded without stretching or twisting the facets, and have the compactly flat-folded configuration, which makes it to have great potential in engineering applications.

Accuracy Analysis of Parallel Manipulators With Joint Clearance

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Jian Meng ◽  
Dongjun Zhang ◽  
Zexiang Li
Keyword(s):  
Parallel Manipulator ◽  
Optimization Problem ◽  
Parallel Manipulators ◽  
Joint Clearance ◽  
Error Prediction ◽  
Accuracy Analysis ◽  
Analysis Problem ◽  
Convex Optimization Problem ◽  
End Effector ◽  
Position And Orientation

Due to joint clearance, a parallel manipulator’s end-effector exhibits position and orientation (or collectively referred to as pose) errors of various degrees. This paper aims to provide a systematic study of the error analysis problem for a general parallel manipulator influenced by joint clearance. We propose an error prediction model that is applicable to planar or spatial parallel manipulators that are either overconstrained or nonoverconstrained. By formulating the problem as a standard convex optimization problem, the maximal pose error in a prescribed workspace can be efficiently computed. We present several numerical examples to show the applicability and the efficiency of the proposed method.

Generalized Jacobian Analysis of Parallel Manipulators With Multiple End-Effectors

2014 ◽  
Author(s):  
Antonius G. L. Hoevenaars ◽  
Patrice Lambert ◽  
Just L. Herder
Keyword(s):  
Linear Function ◽  
Closed Loop ◽  
Parallel Manipulators ◽  
Terminal Link ◽  
Generalized Jacobian ◽  
End Effector ◽  
End Effectors

This paper presents a methodology for the Jacobian analysis of parallel manipulators with multiple end-effectors (PMxE). The end-effector velocity state of a PMxE is described by one twist of a principal end-effector with respect to the base and a set of relative twists of the remaining end-effectors with respect to the principal end-effector The twist of each terminal link with respect to the principal end-effector is then expressed as a linear function of the relative twists, which enables an extension of the generalized Jacobian analysis to PMxE. The presented methodology is detailed for parallel manipulators with two end-effectors, where a planar 6-RRR manipulator with a 2-RRR internal closed-loop is used as an example.

Path Tracking Experimentation With Epi.q-Mod 2: An Obstacle Climbing Mobile Robot

2016 ◽  
Author(s):  
Giuseppe Quaglia ◽  
Matteo Nisi ◽  
Luca Bruzzone ◽  
Pietro Fanghella
Keyword(s):  
Mobile Robot ◽  
Closed Loop ◽  
Kinematic Model ◽  
Open Loop ◽  
Path Tracking ◽  
Multibody Model ◽  
Experimental Activity ◽  
Robot Trajectory ◽  
Position Controller ◽  
Climbing Ability

In this paper, an experimental activity on the path tracking for a hybrid wheeled-legged mobile robot is presented. The activity has been conducted on the Epi.q-Mod 2 prototype, a mobile robot with obstacle climbing ability. This feature has been obtained using a smart rotating leg architecture. Unfortunately, this solution introduces complexity on the kinematic and dynamic modeling of the robot. In order to understand the behavior of the robot during the motion on a generic trajectory, an open loop position controller has been implemented. In particular, the experimental robot trajectory has been reconstructed from odometric quantities through a simplified kinematic model. This trajectory has been compared with the trajectory obtained from a multibody model of the real prototype in order to evaluate the differences between the two approaches. This activity represents a preliminary step for the development of a self-guidance vehicle. In future works the developed model will be used to provide a position feedback for a closed loop position controller without the necessity to use additional sensors.

Joint Rotation Space, Workspace, and Singularity-Free Workspace of Parallel Five-Bar Manipulators

2000 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Yi Zhang
Keyword(s):  
Trajectory Planning ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
Parallel Manipulators ◽  
Extensive Study ◽  
Open Loop ◽  
Joint Rotation ◽  
One To One ◽  
The One

Abstract Closed-loop manipulators, while offering some advantages over the open-loop manipulators, also introduce new topics of study such as their joint rotation space (JRS) and workspace. In the previous studies, the concept of JRS was very effective in the study of the allowable inputs of five-bar linkages[11], and the concepts of sheet and side[7] were later introduced for the purpose of clearly describing all of the joint rotation spaces associated to a parallel manipulator with two degrees of freedom. However, of the two types of singularity of parallel manipulators, only the uncertainty singularity was considered in the aforementioned studies. The stationarity singularity was not indicated in the JRS of the manipulators, which would not be sufficient in the design and trajectory planning of parallel manipulators where the one-to-one correspondence between the JRS and the wrist point workspace would be required. This paper reports an extensive study on the JRS and singularity-free workspace of the parallel five-bar manipulators. The objective of the study is to establish a one-to-one corresponding relationship between the JRS and singularity-free workspace. A concise and sufficient way is proposed to thoroughly recognize the JRS and workspace of the parallel five-bar manipulators. The result can be applied in the design and trajectory planning of parallel five-bar manipulators, and the concepts can be extended to other parallel manipulators.

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.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

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