Kinematic Calibration of a Three Degrees-of-Freedom Parallel Manipulator With a Laser Tracker

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Leiying He ◽  
Qinchuan Li ◽  
Xubiao Zhu ◽  
Chuanyu Wu
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Mapping Function ◽  
Laser Tracker ◽  
Geometrical Parameters ◽  
Kinematic Calibration ◽  
Positioning Errors ◽  
Calibration Experiment ◽  
Three Degrees Of Freedom

Kinematic calibration is commonly used to improve the accuracy of a parallel mechanism. This paper presents an effective method for calibrating an overconstrained three degrees-of-freedom parallel manipulator employing a direct kinematic model. An error-mapping function is formulated from the differential of its kinematic model which is established through vector chains with the geometrical errors. To simplify the measurement of the error, the positioning and orientation error of the moving platform is replaced by the positioning error of the tool center point, which can be measured by a laser tracker accurately. Three different objective functions F1, F2, and F∞, respectively, representing 1-norm, 2-norm, and inf-norm of the error vector are used to identify the geometrical parameters of the manipulator. The results of computer simulation show that parameters after kinematic calibration through minimizing the objective function F2 is highly accurate and efficient. A calibration experiment is carried out to verify the effectiveness of the method. The maximum residual of calibration points reduces greatly from 3.904 to 0.256 mm during parameter identification. The positioning errors of all points on and inside the space surrounded by the calibration points are smaller than 0.4 mm after error compensation.

A Model of the Human Spine: Forward and Inverse Kinematics

1992 ◽  
Author(s):  
Sunil Kumar Agrawal ◽  
Siyan Li ◽  
Glen Desmier
Keyword(s):  
Range Of Motion ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Joint Angles ◽  
Human Spine ◽  
Forward And Inverse Kinematics ◽  
Position And Orientation ◽  
Three Degrees Of Freedom ◽  
Adjacent Vertebra

Abstract The human spine is a sophisticated mechanism consisting of 24 vertebrae which are arranged in a series-chain between the pelvis and the skull. By careful articulation of these vertebrae, a human being achieves fine motion of the skull. The spine can be modeled as a series-chain with 24 rigid links, the vertebrae, where each vertebra has three degrees-of-freedom relative to an adjacent vertebra. From the studies in the literature, the vertebral geometry and the range of motion between adjacent vertebrae are well-known. The objectives of this paper are to present a kinematic model of the spine using the available data in the literature and an algorithm to compute the inter vertebral joint angles given the position and orientation of the skull. This algorithm is based on the observation that the backbone can be described analytically by a space curve which is used to find the joint solutions..

Visual servoing framework using Gaussian process for an aerial parallel manipulator

2018 ◽  
Vol 233 (9) ◽  
pp. 3408-3425
Author(s):  
Sungwook Cho ◽  
David Hyunchul Shim
Keyword(s):  
Gaussian Process ◽  
Parallel Manipulator ◽  
Visual Servoing ◽  
Degrees Of Freedom ◽  
Flight Test ◽  
Control Input ◽  
Body Velocity ◽  
Aerial Vehicle ◽  
Three Degrees Of Freedom ◽  
Traditional Image

This paper proposes a Gaussian process based visual servoing framework for an aerial parallel manipulator. Our aerial parallel manipulator utilizes the on-board eye-in-hand vision sensor system attached on the end-effector of three-degrees-of-freedom parallel manipulator. There are three major advantages: small, light in weight, and linearity with respect to the host vehicle rather than the serial manipulator, but it has a critical drawback that its workspace is too small to perform the mission itself during the hovering. In order to overcome the limited workspace problem and perform the mission more actively, proposed visual servoing framework is proposed to generate relative body velocity commands of the host vehicle by using the interpolated and extrapolated feature path between the initial and desired features to fed into the underactuated aerial parallel manipulator. It can generate not only numerical stable but also feasible control input. Furthermore, it can overcome the weakness of the traditional image-based visual servoing such as singularities, uncertainties, and local minimums during calculating image Jacobian under the large disparity environment between the target and the unmanned aerial vehicle. As a result of the proposed contribution, we show that our contribution is reliable to perform the picking-and-replacement autonomously, and it shows that it can be applied in the large displacement environments throughout the flight test.

scholarly journals A robomech class parallel manipulator with three degrees of freedom

2020 ◽  
Vol 3 (7 (105)) ◽  
pp. 44-56
Author(s):  
Zhumadil Baigunchekov ◽  
Azamat Mustafa ◽  
Tarek Sobh ◽  
Sarosh Patel ◽  
Muratulla Utenov
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Three Degrees Of Freedom

Potential of the 3-UPU Translational Parallel Manipulator

2010 ◽  
Author(s):  
Ahmed Hachem Chebbi ◽  
Vincenzo Parenti-Castelli
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Joint Clearance ◽  
General Frame ◽  
Pure Rotation ◽  
Work Done ◽  
Relevant Work ◽  
Three Degrees Of Freedom

The 3-UPU three degrees of freedom fully parallel manipulator, where U and P are for universal and prismatic pair respectively, is a very well known manipulator that can provide the platform with three degrees of freedom of pure translation, pure rotation or mixed translation and rotation according to the relative directions of the revolute axes. Many studies have been reported in the literature on singularities, workspace and joint clearance influence on the platform accuracy of this manipulator. However, much work has still to be done to reveal all the features this topology can offer to the designer. This paper collects the previous most relevant work done on the 3-UPU parallel manipulator and shows the main results in a coherent general frame. The paper proposes new architectures of the 3-UPU manipulator which offer interesting features to the designer. Finally, based on a number of indexes, a procedure is proposed that allows the designer to select the best architecture of the 3-UPU manipulator for a given task.

Optimal Design of the Three-Degree-of-Freedom Parallel Manipulator in a Spray-Painting Equipment

Robotica ◽  
2019 ◽  
Vol 38 (6) ◽  
pp. 1064-1081
Author(s):  
Guang Yu ◽  
Jun Wu ◽  
Liping Wang ◽  
Ying Gao
Keyword(s):  
Optimal Design ◽  
Parallel Manipulator ◽  
Optimization Design ◽  
Virtual Work ◽  
Kinematic Model ◽  
Geometrical Parameters ◽  
Parallel Mechanisms ◽  
Spray Painting ◽  
Conditioning Performance ◽  
Accuracy Performance

SUMMARYSpray-painting equipments are important for the automatic spraying of long conical objects such as rocket fairing. This paper proposes a spray-painting equipment that consists of a feed worktable, a gantry frame and two serial–parallel mechanisms and investigates the optimal design of PRR–PRR parallel manipulator in serial–parallel mechanisms. Based on the kinematic model of the parallel manipulator, the conditioning performance, workspace and accuracy performance indices are defined. The dynamic model is derived using virtual work principle and dynamic evaluation index is defined. The conditioning performance, workspace, accuracy performance and dynamic performance are involved in multi-objective optimization design to determine the optimal geometrical parameters of the parallel manipulator. Furthermore, the geometrical parameters of the gantry frame are optimized. An example is given to show how to determine these parameters by taking a long object with conical surface as painted object.

A Measure for Evaluation of Maximum Acceleration of Redundant and Nonredundant Parallel Manipulators

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Jun Wu ◽  
Binbin Zhang ◽  
Liping Wang
Keyword(s):  
Dynamic Model ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Virtual Work ◽  
Parallel Manipulators ◽  
Maximum Acceleration ◽  
Virtual Work Principle ◽  
Joint Force ◽  
Joint Forces ◽  
Three Degrees Of Freedom

The paper deals with the evaluation of acceleration of redundant and nonredundant parallel manipulators. The dynamic model of three degrees-of-freedom (3DOF) parallel manipulator is derived by using the virtual work principle. Based on the dynamic model, a measure is proposed for the acceleration evaluation of the redundant parallel manipulator and its nonredundant counterpart. The measure is designed on the basis of the maximum acceleration of the mobile platform when one actuated joint force is unit and other actuated joint forces are less than or equal to a unit force. The measure for evaluation of acceleration can be used to evaluate the acceleration of both redundant parallel manipulators and nonredundant parallel manipulators. Furthermore, the acceleration of the 4-PSS-PU parallel manipulator and its nonredundant counterpart are compared.

A Calibration Method for a Three-Degrees-of-Freedom Parallel Manipulator with a Redundant Passive Chain

2012 ◽  
Vol 162 ◽  
pp. 171-178 ◽  
Author(s):  
Takaaki Oiwa ◽  
Harunaho Daido ◽  
Junichi Asama
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Least Squares Method ◽  
Coordinate Measuring Machine ◽  
Calibration Method ◽  
Displacement Sensor ◽  
Measurement Experiment ◽  
Measuring Machine ◽  
Measured Length ◽  
Three Degrees Of Freedom

This paper deals with parameter identification for a three-degrees-of-freedom (3-DOF) parallel manipulator, based on measurement redundancy. A redundant passive chain with a displacement sensor connects the moving stage to the machine frame. The passive chain is sequentially placed in three directions at approximately right angles to one another to reliably detect the motion of the stage. Linear encoders measure changes in lengths of the passive chain and the three actuated chains of the manipulator during traveling of the moving stage. Comparison between the measured length and the length calculated from forward kinematics of the 3-DOF manipulator reveals a length error of the passive chain. The least-squares method using a Jacobian matrix corrects 27 kinematic parameters so that the length errors of the passive chain are minimized. The above calculations were accomplished in both numerical simulations and experiments employing a coordinate measuring machine based on the parallel manipulator. Moreover, a length measurement simulation of gauge block measurement and a measurement experiment using the measuring machine were performed to verify the identified parameters.

Helical Kirigami-Enabled Centimeter-Scale Worm Robot With Shape-Memory-Alloy Linear Actuators

2015 ◽  
Vol 7 (2) ◽  
Author(s):  
Ketao Zhang ◽  
Chen Qiu ◽  
Jian S. Dai
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Kinematic Model ◽  
Parallel Structure ◽  
Geometrical Parameters ◽  
Parallel Structures ◽  
Complete Procedure ◽  
Motion Characteristics

The wormlike robots are capable of imitating amazing locomotion of slim creatures. This paper presents a novel centimeter-scale worm robot inspired by a kirigami parallel structure with helical motion. The motion characteristics of the kirigami structure are unravelled by analyzing the equivalent kinematic model in terms of screw theory. This reveals that the kirigami parallel structure with three degrees-of-freedom (DOF) motion is capable of implementing both peristalsis and inchworm-type motion. In light of the revealed motion characteristics, a segmented worm robot which is able to imitate contracting motion, bending motion of omega shape and twisting motion in nature is proposed by integrating kirigami parallel structures successively. Following the kinematic and static characteristics of the kirigami structure, actuation models are explored by employing the linear shape-memory-alloy (SMA) coil springs and the complete procedure for determining the geometrical parameters of the SMA coil springs. Actuation phases for the actuation model with two SMA springs are enumerated and with four SMA springs are calculated based on the Burnside's lemma. In this paper, a prototype of the worm robot with three segments is presented together with a paper-made body structure and integrated SMA coil springs. This centimeter-scale prototype of the worm robot is lightweight and can be used in confined environments for detection and inspection. The study presents an interesting approach of integrating SMA actuators in kirigami-enabled parallel structures for the development of compliant and miniaturized robots.

scholarly journals A Kinematic Calibration Method of a 3T1R 4-Degree-of-Freedom Symmetrical Parallel Manipulator

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 357
Author(s):  
Fengxuan Zhang ◽  
Silu Chen ◽  
Yongyi He ◽  
Guoyun Ye ◽  
Chi Zhang ◽  
...  
Keyword(s):  
Parallel Manipulator ◽  
Kinematic Model ◽  
Calibration Method ◽  
Error Modeling ◽  
Degree Of Freedom ◽  
Least Square ◽  
Kinematic Calibration ◽  
Recursive Least Square ◽  
Local Product ◽  
Branched Chain

This paper proposes a method for kinematic calibration of a 3T1R, 4-degree-of-freedom symmetrical parallel manipulator driven by two pairs of linear actuators. The kinematic model of the individual branched chain is established by using the local product of exponentials formula. Based on this model, the model of the end effector’s pose error is established from a pair of symmetrical branched chains, and a recursive least square method is applied for the parameter identification. By installing built-in sensors at the passive joints, a calibration method for a serial manipulator is eventually extended to this parallel manipulator. Specifically, the sensor installed at the second revolute joint of each branched chain is saved, replaced by numerical calculation according to kinematic constraints. The simulation results validate the effectiveness of the proposed kinematic error modeling and identification methods. The procedure for pre-processing compensation on this 3T1R parallel manipulator is eventually given to improve its absolute positioning accuracy, using the inverse of the calibrated kinematic model.

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