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 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.

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 A Novel Three-Loop Parallel Robot With Full Mobility: Kinematics, Singularity, Workspace, and Dexterity Analysis

2017 ◽  
Vol 9 (5) ◽  
Author(s):  
Wei Li ◽  
Jorge Angeles
Keyword(s):  
High Speed ◽  
Screw Theory ◽  
Parallel Robot ◽  
Simple Expression ◽  
Parallel Robots ◽  
Forward Displacement ◽  
Design Variables ◽  
The Subject ◽  
Stewart Gough Platform ◽  
The Given

A novel parallel robot, dubbed the SDelta, is the subject of this paper. SDelta is a simpler alternative to both the well-known Stewart–Gough platform (SGP) and current three-limb, full-mobility parallel robots, as it contains fewer components and all its motors are located on the base. This reduces the inertial load on the system, making it a good candidate for high-speed operations. SDelta features a symmetric structure; its forward-displacement analysis leads to a system of three quadratic equations in three unknowns, which admits up to eight solutions, or half the number of those admitted by the SGP. The kinematic analysis, undertaken with a geometrical method based on screw theory, leads to two Jacobian matrices, whose singularity conditions are investigated. Instead of using the determinant of a 6 × 6 matrix, we derive one simple expression that characterizes the singularity condition. This approach is also applicable to a large number of parallel robots whose six actuation wrench axes intersect pairwise, such as all three-limb parallel robots whose limbs include, each, a passive spherical joint. The workspace is analyzed via a geometric method, while the dexterity analysis is conducted via discretization. Both show that the given robot has the potential to offer both large workspace and good dexterity with a proper choice of design variables.

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.

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.

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.

scholarly journals NAVARO II, a Novel Scissor-Based Planar Parallel Robot1

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
Damien Chablat ◽  
Luc Rolland
Keyword(s):  
Geometric Property ◽  
Kinematic Model ◽  
Parallel Robot ◽  
Inverse Kinematic ◽  
Mobile Platform ◽  
Compact Form ◽  
Revolute Joint ◽  
Actuation Mechanism ◽  
Working Space ◽  
Orthogonal Plane

This article presents a new variable actuation mechanism based on the 3-RPR parallel robot. This mechanism is an evolution of the NaVARo robot, a 3-RRR parallel robot, for which the second revolute joint of the three legs is replaced by a scissor to obtain a larger working space and avoid the use of parallelograms to operate the second revolute joint. To obtain better spatial rigidity, the leg mechanism is constructed by placing the scissors in an orthogonal plane to the plane of the manipulator displacement (3-RRR or even the 3-RPR). This geometric property brings the significant consequence of allowing the scissors to directly substitute the prismatic chains in the 3-RPR and enjoy the same kinematics advantages for the overall robots as only one solution to the inverse kinematic model. From the Jacobian expression, surfaces of singularity can be calculated and presented in a compact form. The singularity equations are presented for a robot with a similar base and mobile platform. The properties of the scissors are then determined to have a prescribed regular workspace.

scholarly journals Empirical Quasi-Static and Inverse Kinematics of Cable-Driven Parallel Manipulators Including Presence of Sagging

2020 ◽  
Vol 10 (15) ◽  
pp. 5318
Author(s):  
Phan Gia Luan ◽  
Nguyen Truong Thinh
Keyword(s):  
Kinematic Model ◽  
Static Problem ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Inverse Kinematic ◽  
Inverse Kinematic Problem ◽  
Redundant Actuators ◽  
Small Change ◽  
Feasible Solutions ◽  
Flexible Cables

Cable-driven parallel manipulators (CDPMs) have been of great interest to researchers in recent years because they have many advantages compared to the traditional parallel robot. However, in many studies they lack the cable’s elasticity that leads to flexible cables just being considered as extendable rigid links. Furthermore, an external force acts on the extremities of cable and the self-weight is relevant to the length of it. Experimentally, a small change in length produces a huge change in tension act on the entire cable. By this property, the adjusting length of cable is often added to the traditional inverse kinematic solution in order to reduce the tension force exerted on the cable. This means that the load on the actuator is also reduced. Because of the relationship between tension that acts on the cable and its length, the kinematic problem itself does not make sense without concerning the static or dynamic problems. There is often interest in planning forces for actuators and the length of cables based on a given quasi-static trajectory of the moving platform. The mentioned problem is combined with the quasi-static problem with the inverse kinematic problem of CDPM. In this study, we introduce a novel procedure to produce the quasi-static model and inverse kinematic model for CDPM with the presence of sagging by using both an analytic approach and empirical approach. The produced model is time-efficient and is generalized for spatial CDPM. To illustrate the performance of the proposed model, the numerical and experimental approaches are employed to determine particular solutions in the feasible solutions set produced by our model in order to control the two redundant actuators’ CDPM tracking on a certain desired trajectory. Its results are clearly described in the experimental section.

scholarly journals Design and implementation of a multi-degrees-of-freedom cable-driven parallel robot with gripper

2018 ◽  
Vol 15 (5) ◽  
pp. 172988141880384 ◽  
Author(s):  
Jonqlan Lin ◽  
Chi Ying Wu ◽  
Julian Chang
Keyword(s):  
Degrees Of Freedom ◽  
Load Capacity ◽  
Kinematic Model ◽  
Weight Ratio ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Control Mode ◽  
Level Control ◽  
End Effector ◽  
Upper Level

Cable-driven parallel robots comprise driven actuators that allow controlled cables to act in parallel on an end-effector. Such a robotic system has a potentially large reachable workspace, large load capacity, high payload-to-weight ratio, high reconfigurability, and low inertia, relative to rigid link serial and parallel robots. In this work, a multi-degrees-of-freedom cable-suspended robot that can carry out pick-and-place tasks in large workspaces with heavy loads is designed. The proposed cable-driven parallel robot is composed of a rigid frame and an end-effector that is suspended from eight cables—four upper cables and four lower cables. The lengths of the cables are computed from the given positions of the suspended end-effector using a kinematic model. However, most multi-cable-driven robots suffer from interference among the cables, requiring a complex control methodology to find a target goal. Owing to this issue with cable-driven parallel robots, the whole control structure decomposes positioning control missions and allocates them into upper level and lower level. The upper level control is responsible for tracking the suspended end-effector to the target region. The lower level control makes fine positional modifications. Experimental results reveal that the hybrid control mode notably improves positioning performance. The wide variety of issues that are considered in this work apply to aerostats, towing cranes, locomotion interfaces, and large-scale manufacturing that require cable-driven parallel robots.

Hybrid Approach to Modeling a Flexible Parallel Robot for Vibration Damping

2007 ◽  
Author(s):  
Jens Kroneis ◽  
Steven Liu
Keyword(s):  
Dynamic Models ◽  
Kinematic Model ◽  
Hybrid Approach ◽  
Measurement Data ◽  
Parallel Robot ◽  
Vibration Damping ◽  
Parallel Robots ◽  
Body Kinematic ◽  
Verification Process ◽  
Standard Frame

In this paper a new method for derivation and verification of rigid and flexible body kinematic and dynamic models of complex parallel robots including crank mechanisms is presented. The rigid body kinematic model is based on standard frame transformations and involves holonomic constraints. Lagrange’s equations of the first type are used for the dynamic modeling of the rigid structure. Using Euler-Bernoulli beams and assumed modes method, a new concept for deriving flexible kinematics and dynamics is developed considering configuration-dependent end masses, called effective payloads. Furthermore a vibration analysis is accomplished and a vibration damping strategy for the parallel robot based on input shaping is described. Through the whole verification process MSC.ADAMS models and measurement data of the demonstrator SpiderMill are used.

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