scholarly journals On the Minimum Cable Tensions for the Cable-Based Parallel Robots

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Peng Liu ◽  
Yuanying Qiu ◽  
Yu Su ◽  
Jiantao Chang
Keyword(s):  
Convex Optimization ◽  
Optimization Algorithm ◽  
Kinematic Model ◽  
Optimization Theory ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Performance Indices ◽  
Cable Tension ◽  
The Stability ◽  
The Relationship

This paper investigates the minimum cable tension distributions in the workspace for cable-based parallel robots to find out more information on the stability. First, the kinematic model of a cable-based parallel robot is derived based on the wrench matrix. Then, a noniterative polynomial-based optimization algorithm with the proper optimal objective function is presented based on the convex optimization theory, in which the minimum cable tension at any pose is determined. Additionally, three performance indices are proposed to show the distributions of the minimum cable tensions in a specified region of the workspace. An important thing is that the three performance indices can be used to evaluate the stability of the cable-based parallel robots. Furthermore, a new workspace, the Specified Minimum Cable Tension Workspace (SMCTW), is introduced, within which all the minimum tensions exceed a specified value, therefore meeting the specified stability requirement. Finally, a camera robot parallel driven by four cables for aerial panoramic photographing is selected to illustrate the distributions of the minimum cable tensions in the workspace and the relationship between the three performance indices and the stability.

scholarly journals Motion Reliability Analysis of the Delta Parallel Robot considering Mechanism Errors

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Yu Li ◽  
Deyong Shang ◽  
Xun Fan ◽  
Yue Liu
Keyword(s):  
Reliability Analysis ◽  
Structural Parameters ◽  
Kinematic Model ◽  
Vertical Direction ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Joint Clearance ◽  
Spherical Joint ◽  
Key Factor ◽  
The Relationship

Delta parallel robots are widely used in assembly detection, packaging sorting, precision positioning, and other fields. With the widespread use of robots, people have increasing requirements for motion accuracy and reliability. This paper considers the influence of various mechanism errors on the motion accuracy and analyzes the motion reliability of the mechanism. Firstly, we establish a kinematic model of the robot and obtain the relationship between the position of the end effector and the structural parameters based on the improved D–H transform rule. Secondly, an error model considering the dimension error, the error of revolute joint clearance, driving error, and the error of spherical joint clearance is established. Finally, taking an actual robot as an example, the comprehensive influence of mechanism errors on motion accuracy and reliability in different directions is quantitatively analyzed. It is shown that the driving error is a key factor determining the motion accuracy and reliability. The influence of mechanism errors on motion reliability is different in different directions. The influence of mechanism errors on reliability is small in the vertical direction, while it is great in the horizontal direction. Therefore, we should strictly control the mechanism errors, especially the driving angle, to ensure the motion accuracy and reliability. This research has significance for error compensation, motion reliability analysis, and reliability prediction in robots, and the conclusions can be extended to similar mechanisms.

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.

scholarly journals Control of a 3-RRR Planar Parallel Robot Using Fractional Order PID Controller

2020 ◽  
Vol 17 (6) ◽  
pp. 822-836
Author(s):  
Auday Al-Mayyahi ◽  
Ammar A. Aldair ◽  
Chris Chatwin
Keyword(s):  
Fractional Order ◽  
Material Handling ◽  
State Of The Art ◽  
Kinematic Model ◽  
Parallel Robot ◽  
Inverse Kinematic ◽  
Open Loop ◽  
Parallel Robots ◽  
The State ◽  
Revolute Joints

Abstract3-RRR planar parallel robots are utilized for solving precise material-handling problems in industrial automation applications. Thus, robust and stable control is required to deliver high accuracy in comparison to the state of the art. The operation of the mechanism is achieved based on three revolute (3-RRR) joints which are geometrically designed using an open-loop spatial robotic platform. The inverse kinematic model of the system is derived and analyzed by using the geometric structure with three revolute joints. The main variables in our design are the platform base positions, the geometry of the joint angles, and links of the 3-RRR planar parallel robot. These variables are calculated based on Cayley-Menger determinants and bilateration to determine the final position of the platform when moving and placing objects. Additionally, a proposed fractional order proportional integral derivative (FOPID) is optimized using the bat optimization algorithm to control the path tracking of the center of the 3-RRR planar parallel robot. The design is compared with the state of the art and simulated using the Matlab environment to validate the effectiveness of the proposed controller. Furthermore, real-time implementation has been tested to prove that the design performance is practical.

scholarly journals Potential Energy Distribution of Redundant Cable-Driven Robot Applied to Compliant Grippers: Method and Computational Analysis

Sensors ◽  
2019 ◽  
Vol 19 (15) ◽  
pp. 3403 ◽  
Author(s):  
Rodriguez-Barroso ◽  
Saltaren ◽  
Portilla ◽  
Cely ◽  
Yakrangi
Keyword(s):  
Energy Distribution ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Potential Energy Distribution ◽  
End Effector ◽  
Tension Distribution ◽  
Multibody Dynamic ◽  
Compliant Actuators ◽  
Dynamic Software ◽  
The Relationship

Cable-driven parallel robots with a redundant configuration have infinite solutions for their cable tension distribution to provide a specific wrench to the end-effector. Redundancy is commonly used to increase the workspace and stiffness or to achieve secondary objectives like energetic minimization or additional movements. This article presents a method based on energy distribution to handle the redundancy of cable-driven parallel robots. This method allows the deformation and tension of each link to be related to the total energy available in the parallel robot. The study of energy distribution expression allows deformation, tension, and position to be combined. It also defines the range of tension and deformation that cables can achieve without altering the wrench exerted on the end-effector. This range is used with a passive reconfigurable end-effector to control the position of two grippers attached to some cables which act as compliant actuators. The relationship between the actuators’ energy and their corresponding gripper positions is also provided. In this way, energy measurement from the actuators allows the grasping state to be sensed. The results are validated using multibody dynamic software.

Kinematic uncertainty analysis of a cable-driven parallel robot based on an error transfer model

2021 ◽  
pp. 1-23
Author(s):  
Jun Gao ◽  
Bin Zhou ◽  
Bin Zi ◽  
Sen Qian ◽  
Ping Zhao
Keyword(s):  
Uncertainty Analysis ◽  
Kinematic Model ◽  
Evidence Theory ◽  
Parallel Robot ◽  
Fast Response ◽  
Inverse Kinematic ◽  
Parallel Robots ◽  
Transfer Model ◽  
The Given ◽  
Error Transfer

Abstract Cable-driven parallel robots (CDPRs) are a kind of mechanism with large workspace, fast response, and low inertia. However, due to the existence of fixed pulleys, it is unavoidable to bring uncertain cable lengths and lead to pose errors of the end-effector (EE). The inverse kinematic model of a CDPR for picking up medicines is established by considering radii of fixed pulleys. The influence of radii of fixed pulleys on errors of cable lengths is explored. Error transfer model of the CPDR is constructed, and uncertain sources of cable lengths are analyzed. Based on evidence theory and error transfer model, an evidence theory-based uncertainty analysis method (ETUAM) is presented. The structural performance function for kinematic response is derived based on error transfer model. Belief and plausibility measures of joint focal elements under the given threshold are obtained. Kinematic error simulations show that errors of cable lengths become larger with the increase of radii of fixed pulleys. Compared with the vertex method and Monte Carlo method, numerical examples demonstrate the accuracy and efficiency of the ETUAM when it comes to the kinematic uncertainty analysis of the CDPR.

scholarly journals Modeling Parallel Robot Kinematics for 3T2R and 3T3R Tasks Using Reciprocal Sets of Euler Angles

Robotics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 68 ◽  
Author(s):  
Moritz Schappler ◽  
Svenja Tappe ◽  
Tobias Ortmaier
Keyword(s):  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Robot Kinematics ◽  
Euler Angles ◽  
Gradient Descent Algorithm ◽  
Kinematic Models ◽  
Rotational Degrees Of Freedom ◽  
Definition Of

Industrial manipulators and parallel robots are often used for tasks, such as drilling or milling, that require three translational, but only two rotational degrees of freedom (“3T2R”). While kinematic models for specific mechanisms for these tasks exist, a general kinematic model for parallel robots is still missing. This paper presents the definition of the rotational component of kinematic constraints equations for parallel robots based on two reciprocal sets of Euler angles for the end-effector orientation and the orientation residual. The method allows completely removing the redundant coordinate in 3T2R tasks and to solve the inverse kinematics for general serial and parallel robots with the gradient descent algorithm. The functional redundancy of robots with full mobility is exploited using nullspace projection.

Sliding Mode Set Point Control of a Six-DOF Cable-Suspended Parallel Robot With Tension Constraints and Uncertain Disturbances

2018 ◽  
Author(s):  
Ping Ren ◽  
Yunlong Sun
Keyword(s):  
Sliding Mode ◽  
Sufficient Conditions ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Set Point ◽  
Uncertain Disturbances ◽  
Point Motion ◽  
Six Dof ◽  
Six Degree Of Freedom ◽  
The Relationship

This paper presents the design of a robust sliding mode controller for a six-degree-of-freedom cable-suspended parallel robot under uncertain disturbances. The control of cable-suspended parallel robots is quite challenging due to the unidirectional constraint of cable tensions. With the aid of interval analysis, a set of algebraic inequalities is obtained to establish the relationship between the cables’ tension constraints and the controller parameters. The sufficient conditions of the controller parameters satisfying the constraints are obtained for the set point motion within the robot’s static workspace. Numerical simulations are presented to verify the effectiveness of the proposed approach.

The rigid S-type cable-suspended parallel robot design, modelling and analysis

Robotica ◽  
2014 ◽  
Vol 34 (9) ◽  
pp. 1948-1960 ◽  
Author(s):  
M. Filipovic ◽  
A. Djuric ◽  
Lj. Kevac
Keyword(s):  
Jacobian Matrix ◽  
Virtual Work ◽  
Kinematic Model ◽  
Parallel Robot ◽  
Model Verification ◽  
Robot Design ◽  
Principle Of Virtual Work ◽  
Lagrange Principle ◽  
Internal Forces ◽  
The Relationship

SUMMARYThis paper presents design, modelling and analysis of the selected Rigid ropes S-type Cable-suspended Parallel Robot (RSCPR). The characteristic of this system is its geometric construction which defines the kinematic model through the Jacobian matrix. The relationship between external and internal forces is defined by the Lagrange principle of virtual work. The Jacobian matrix is directly involved in the application of the Lagrange principle of virtual work and generation of the dynamic model of the RSCPR system. Selected examples of the CPR system types are analysed and the comparison of their results is presented. The software package named ORIGI has been developed for the RSCPR model verification.

scholarly journals Design of a Planar Cable-Driven Parallel Robot for Non-Contact Tasks

2021 ◽  
Vol 11 (20) ◽  
pp. 9491
Author(s):  
Valentina Mattioni ◽  
Edoardo Ida’ ◽  
Marco Carricato
Keyword(s):  
Large Scale ◽  
Kinematic Model ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Guidance System ◽  
Small Scale ◽  
Laser Engraving ◽  
Mechanical Structure ◽  
Novel Concept ◽  
Contact Tasks

Cable-driven parallel robots offer significant advantages in terms of workspace dimensions and payload capability. Their mechanical structure and transmission system consist of light and extendable cables that can withstand high tensile loads. Cables are wound and unwound by a set of motorized winches, so that the robot workspace dimensions mainly depend on the amount of cable that each drum can store. For this reason, these manipulators are attractive for many industrial tasks to be performed on a large scale, such as handling, pick-and-place, and manufacturing, without a substantial increase in costs and mechanical complexity with respect to a small-scale application. This paper presents the design of a planar overconstrained cable-driven parallel robot for quasi-static non-contact operations on planar vertical surfaces, such as laser engraving, inspection and thermal treatment. The overall mechanical structure of the robot is shown, by focusing on the actuation and guidance systems. A novel concept of the cable guidance system is outlined, which allows for a simple kinematic model to control the manipulator. As an application example, a laser diode is mounted onto the end-effector of a prototype to perform laser engraving on a paper sheet. Observations on the experiments are reported and discussed.

Sliding Mode Set-Point Control of a Three-DOF Cable-Suspended Parallel Robot With Uncertain Mass and Disturbances

2019 ◽  
Author(s):  
Ping Ren ◽  
Xu Sheng
Keyword(s):  
Sliding Mode ◽  
Sufficient Conditions ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Parallel Mechanisms ◽  
Set Point ◽  
Point Motion ◽  
Actuation Scheme ◽  
Three Degree Of Freedom ◽  
The Relationship

Abstract Cable-Suspended Parallel Robots (CSPRs) utilize winches and cables as the actuation scheme instead of rigid links, which renders them advantages of both parallel mechanisms and cable mechanisms. In this paper, a robust sliding mode controller was designed for a three-degree-of-freedom CSPR with uncertain end-effector mass and external disturbances. To control the motions of CSPRs is usually challenging due to the unidirectional constraints of cable tensions. Based on interval analysis, a set of analytical inequalities is obtained which establish the relationship between the cables’ tension constraints and the controller parameters. The sufficient conditions of the controller parameters satisfying the constraints are obtained for the set-point motion subject to uncertainties. Numerical simulations are presented to verify the effectiveness of the proposed approach.

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