Complete, Minimal and Continuous Kinematic Error Models of Perfect Multi-DOF Joints for Parallel Manipulators

2020 ◽  
Author(s):  
Lingyu Kong ◽  
Genliang Chen ◽  
Zhuang Zhang ◽  
Anhuan Xie ◽  
Hao Wang ◽  
...  
Keyword(s):  
Parallel Manipulators ◽  
Error Model ◽  
Parallel Robots ◽  
Kinematic Error ◽  
Kinematic Calibration ◽  
Calibration Result ◽  
Calibration Methods ◽  
Manufacturing Errors ◽  
The One ◽  
Serial Chains

Abstract Kinematic error model plays an important role in improving the positioning accuracy of robot manipulators by kinematic calibration. In order to get a better calibration result, the error model should satisfy complete, minimal and continuous criteria. In order to meet the complete requirement, the multi degree-of-freedom (DOF) joints, such as universal or spherical joint in parallel robots, have to be regarded as serial chains formed by multiple independent single DOF joints, such that the manufacturing errors of these joints can be considered. However, several previous work found that these manufacturing errors for some parallel manipulators have little effect on the accuracy improvement. Besides, considering these kind of errors will cause the kinematics to be much more complicated. Therefore, under the assumptions of perfectly manufactured universal, spherical and cylinder joints, a complete, minimal and continuous (CMC) error model is presented in this paper. The identifiability of the kinematic errors of these multi-DOF joints are analytically analyzed. In order to verify the correctness and effectiveness of the proposed method, a numerical simulation of kinematic calibration is conducted on a 6-UPS parallel manipulator. The calibration result is also compared to the one derived from the error model with 138 error parameters. Since the error model and calibration methods are described uniformly, it can be applied to most parallel manipulators.

A Comprehensive Numerical Study on the Number of Identifiable Kinematic Parameters of Parallel Mechanisms

2021 ◽  
Author(s):  
Lingyu Kong ◽  
Genliang Chen ◽  
Guanyu Huang ◽  
Sumian Song ◽  
Anhuan Xie ◽  
...  
Keyword(s):  
Numerical Study ◽  
Error Model ◽  
Error Modeling ◽  
Kinematic Error ◽  
Kinematic Calibration ◽  
Parallel Mechanisms ◽  
Kinematic Parameters ◽  
Positioning Accuracy ◽  
Prismatic Joints ◽  
Kinematic Error Model

Abstract Kinematic error model plays an important role in improving the positioning accuracy of robot manipulators by kinematic calibration. The identifiability of kinematic parameters in the error model directly affects the positioning accuracy of the mechanism. And the number of identifiable kinematic parameters determines how many parameters can be accurately identified by kinematic calibration, which is one of the theoretical basis of kinematic error modeling. For serial mechanisms, a consensus has been reached that the maximum number of identifiable kinematic parameters is 4R + 2P + 6, where R and P represent the numbers of revolute and prismatic joints, respectively. Due to complex topologies of parallel mechanisms, there is still no agreement on the formula of the maximum number of identifiable parameters. In this paper, a comprehensive numerical study on the number of identifiable kinematic parameters of parallel mechanisms is conducted. The number of identifiable parameters of 3802 kinds of limbs with different types or actuation arrangements are analyzed. It can be concluded that the maximum number of identifiable kinematic parameters is Σ i = 1 n 4Ri + 2Pi + 6 − Ci − 2(PP)i/3(PPP1)i/(2Ri + 2Pi)(PPP)i, where Ci represents the number of joints whose motion cannot be measured and n denotes the number of limbs in a parallel mechanism; (PP)i, (PPP1)i, and (PPP)i represent two consecutive unmeasurable P joints, three consecutive P joints in which two of them cannot be measured, and three unmeasurable P joints, respectively.

Isoconstrained Parallel Generators of Schoenflies Motion

2011 ◽  
Vol 3 (2) ◽  
Author(s):  
Chung-Ching Lee ◽  
Jacques M. Hervé
Keyword(s):  
Parallel Manipulators ◽  
End Effector ◽  
Geometric Conditions ◽  
Algebraic Properties ◽  
Manufacturing Errors ◽  
Fixed Base ◽  
Potential Applications ◽  
Composition Product ◽  
In The Beginning ◽  
Serial Chains

Based on the Lie-group-algebraic properties of the displacement set, the 4DOF primitive generators of the Schoenflies motion termed X-motion for brevity are briefly recalled. An X-motion includes 3DOF spatial translation and any 1DOF rotation provided that the axes are parallel to a given direction. The serial concatenation of two generators of 4DOF X-motion produces a 5DOF motion called double Schoenflies motion or X-X-motion for brevity, which includes 3DOFs of translations and any 2DOFs of rotations if the axes are parallel to two independent vectors. This is established using the composition product of two Lie subgroups of X-motion. All possible 5DOF serial chains with distinct general architectures for the generation of X-X-motion are comprehensively introduced in the beginning. The parallel setting between a fixed base and a moving platform of two 5DOF X-X limbs, under particular geometric conditions, makes up a 4DOF isoconstrained parallel generator (abbreviated as IPG-X) of a Schoenflies motion set. “Isoconstrained” is synonymous with “nonoverconstrianed,” and the corresponding chains are trivial chains of the 6D group of general 6DOF motions and can move in the presence of manufacturing errors. Moreover, related families of IPG-Xs are also deducted by using the reordering or the commutation of the factor method, which yields more 5D subsets of displacements containing also the X-motion of the end effector. In that way, several novel general-type architectures of 4DOF parallel manipulators with potential applications are synthesized systematically in consideration of the actuated pairs near the fixed base.

Kinematic calibration of a 3-PRRU parallel manipulator based on the complete, minimal and continuous error model

2021 ◽  
Vol 71 ◽  
pp. 102158
Author(s):  
Lingyu Kong ◽  
Genliang Chen ◽  
Hao Wang ◽  
Guanyu Huang ◽  
Dan Zhang
Keyword(s):  
Parallel Manipulator ◽  
Error Model ◽  
Kinematic Calibration

scholarly journals A Laser-Based Direct Cable Length Measurement Sensor for CDPRs

Robotics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 60
Author(s):  
Christoph Martin ◽  
Marc Fabritius ◽  
Johannes T. Stoll ◽  
Andreas Pott
Keyword(s):  
Mechanical Design ◽  
Parallel Robots ◽  
Length Measurement ◽  
Cable Length ◽  
Measurement Sensor ◽  
Important Research Topic ◽  
Measurement Principle ◽  
Laser Distance Sensor ◽  
Distance Sensor ◽  
The One

Accuracy improvement is an important research topic in the field of cable-driven parallel robots (*CDPRS). One reason for inaccuracies of *CDPRS are deviations in the cable lengths. Such deviations can be caused by the elongation of the cable due to its elasticity or creep behavior. For most common *CDPRS, the cable lengths are controlled using motor encoders of the winches, without feedback about the actual elongation of the cables. To address this problem, this paper proposes a direct cable length measurement sensor based on a laser distance sensor. We present the mechanical design, the first prototype and an experimental evaluation. As a result, the measurement principle works well and the accuracy of the measured cable lengths is within −2.32 mm to +1.86 mm compared to a range from −5.19 mm to +6.02 mm of the cable length set with the motor encoders. The standard deviation of the cable length error of the direct cable length measurement sensor is 58% lower compared to the one set with the motor encoders. Equipping all cables of the cable robot with direct cable length measurement sensors results in the possibility to correct cable length deviations and thus increase the accuracy of *CDPRS. Furthermore, it enables new possibilities like the automatic recalibration of the home pose.

scholarly journals Introduction to the special issue: parallel manipulators.

Robotica ◽  
1997 ◽  
Vol 15 (4) ◽  
pp. 353-353
Author(s):  
François Pierrot
Keyword(s):  
North America ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Parallel Mechanisms ◽  
Special Issue ◽  
Industrial Areas

It has been a pleasure for me to arrange this Special Issue of Robotica on Parallel Robots which provides 9 papers from authors from Asia, Oceania, North America and Europe; worldwide research on this topic is proof of the growing interest of both the scientific and the industrial areas of parallel mechanisms. I truly believe that the main reason for this enthusiasm is that parallel mechanisms research extends from theoretical mathematics and kinematics to applied robotics, and even beyond, creating new technological challenges.

Variable geometry wing-box: toward a robotic morphing wing.

2021 ◽  
Author(s):  
Amin Moosavian
Keyword(s):  
Degrees Of Freedom ◽  
Minimum Energy ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Optimal Configuration ◽  
Configuration Design ◽  
Variable Geometry ◽  
Static Characteristics ◽  
Actuation Redundancy ◽  
Wing Box

The ability to vary the geometry of a wing to adapt to different flight conditions can significantly improve the performance of an aircraft. However, the realization of any morphing concept will typically be accompanied by major challenges. Specifically, the geometrical constraints that are imposed by the shape of the wing and the magnitude of the air and inertia loads make the usage of conventional mechanisms inefficient for morphing applications. Such restrictions have served as inspirations for the design of a modular morphing concept, referred to as the Variable Geometry Wing-box (VGW). The design for the VGW is based on a novel class of reconfigurable robots referred to as Parallel Robots with Enhanced Stiffness (PRES) which are presented in this dissertation. The underlying feature of these robots is the efficient exploitation of redundancies in parallel manipulators. There have been three categories identified in the literature to classify redundancies in parallel manipulators: 1) actuation redundancy, 2) kinematic redundancy, and 3) sensor redundancy. A fourth category is introduced here, referred to as 4) static redundancy. The latter entails several advantages traditionally associated only with actuation redundancy, most significant of which is enhanced stiffness and static characteristics, without any form of actuation redundancy. Additionally, the PRES uses the available redundancies to 1) control more Degrees of Freedom (DOFs) than there are actuators in the system, that is, under-actuate, and 2) provide multiple degrees of fault tolerance. Although the majority of the presented work has been tailored to accommodate the VGW, it can be applied to any comparable system, where enhanced stiffness or static characteristics may be desired without actuation redundancy. In addition to the kinematic and the kinetostatic analyses of the PRES, which are developed and presented in this dissertation along with several case-studies, an optimal motion control algorithm for minimum energy actuation is proposed. Furthermore, the optimal configuration design for the VGW is studied. The optimal configuration design problem is posed in two parts: 1) the optimal limb configuration, and 2) the optimal topological configuration. The former seeks the optimal design of the kinematic joints and links, while the latter seeks the minimal compliance solution to their placement within the design space. In addition to the static and kinematic criteria required for reconfigurability, practical design considerations such as fail-safe requirements and design for minimal aeroelastic impact have been included as constraints in the optimization process. The effectiveness of the proposed design, analysis, and optimization is demonstrated through simulation and a multi-module reconfigurable prototype.

Kinematic calibration of a laser tracker based on nonlinear optimization of a refined geometric error model

Measurement ◽  
2022 ◽  
pp. 110672
Author(s):  
Xiaopeng Chen ◽  
Yanyang Liu ◽  
Yang Xu ◽  
Siyuan Gou ◽  
Siyan Ma ◽  
...  
Keyword(s):  
Nonlinear Optimization ◽  
Geometric Error ◽  
Error Model ◽  
Laser Tracker ◽  
Kinematic Calibration

A New Kinematic Error Modelling and Identification Method of the Parallel Manipulator

2020 ◽  
Author(s):  
Weitao Li ◽  
Liping Wang
Keyword(s):  
Parallel Manipulators ◽  
Kinematic Error ◽  
Basic Error ◽  
Error Identification ◽  
Partial Differentiation ◽  
Differentiation Method ◽  
Modelling Method ◽  
Error Terms ◽  
Kinematic Error Model ◽  
Identification Model

Abstract Parallel manipulators have broad application prospects on hybrid machine tools. Kinematic error modelling and identification are two key processes to improve the accuracy of parallel manipulators. The traditional kinematic error modelling method adopts the partial differentiation of the ideal kinematic model. However, the partial differentiation method is pure mathematical calculation, which ignores physical meaning of error terms corresponding to each link. In the process of error identification, the Jacobian matrix obtained from the partial differentiation method is usually ill-conditioned, which leads to non-convergence of the identification process. In order to solve the above problems, this paper proposes a new kinematic error modelling method and an error identification model. Firstly, the basic error terms for single link are analyzed. Based on basic error terms, the kinematic error model is established by using the practical connection point of two adjacent links. Then, a new error identification model is derived from the kinematic error model. Finally, as a study case, a 3-DOF parallel tool head is used to verify the correctness of the proposed method. The numerical results show that the proposed method is effective and the accuracy of the 3-DOF parallel tool head improves significantly after compensation of error terms.

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