Stiffness-based trajectory planning of a 6-DOF cable-driven parallel manipulator

2016 ◽  
Vol 231 (21) ◽  
pp. 3999-4011 ◽  
Author(s):  
Wenjia Zhang ◽  
Weiwei Shang ◽  
Bin Zhang ◽  
Fei Zhang ◽  
Shuang Cong
Keyword(s):  
Velocity Profile ◽  
Trajectory Planning ◽  
Parallel Manipulator ◽  
Kinematic Model ◽  
Degree Of Freedom ◽  
Performance Indices ◽  
Curved Trajectories ◽  
Quintic Polynomial ◽  
Point To Point ◽  
Six Degree Of Freedom

The stiffness of the cable-driven parallel manipulator is usually poor because of the cable flexibility, and the existing methods on trajectory planning mainly take the minimum time and the optimal energy into account, not the stiffness. To solve it, the effects of different trajectories on stiffness are studied for a six degree-of-freedom cable-driven parallel manipulator, according to the kinematic model and the dynamic model. The condition number and the minimum eigenvalue of the dimensionally homogeneous stiffness matrix are selected as performance indices to analyze the stiffness changes during the motion. The simulation experiments are implemented on a six degree-of-freedom cable-driven parallel manipulator, to study the stiffness of three different trajectory planning approaches such as S-type velocity profile, quintic polynomial, and trigonometric function. The accelerations of different methods are analyzed, and the stiffness performances for the methods are compared after planning the point-to-point straight and the curved trajectories. The simulation results indicate that the quintic polynomial and S-type velocity profile have the optimal performance to keep the stiffness stable during the motion control and the travel time of the quintic polynomial can be optimized sufficiently while keeping stable.

Geometric Error Compensation With a Six Degree-of–Freedom Rotary Magnetic Actuator

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Alexander Yuen ◽  
Yusuf Altintas
Keyword(s):  
Real Time ◽  
Kinematic Model ◽  
Geometric Error ◽  
Degree Of Freedom ◽  
Geometric Errors ◽  
Working Volume ◽  
Quintic Polynomial ◽  
Gradient Descent Algorithm ◽  
Forward Kinematic ◽  
Six Degree Of Freedom

This paper presents a methodology to compensate the tooltip position errors caused by the geometric errors of a three-axis gantry type micromill integrated with a six degree-of-freedom (6DOF) rotary magnetic table. A geometric error-free ideal forward kinematic model of the nine-axis machine has been developed using homogenous transformation matrices (HTMs). The geometric errors of each linear axis, which include one positioning, two straightness, pitch, roll, and yaw errors, are measured with a laser interferometer and fit to quintic polynomial functions in the working volume of the machine. The forward kinematic model is modified to include the geometric errors which, when subtracted from the ideal kinematic model, gives the deviation between the desired tooltip position with and without geometric errors. The position commands of the six degree-of-freedom rotary magnetic table are modified in real time to compensate for the tooltip deviation using a gradient descent algorithm. The algorithm is simulated and verified experimentally on the nine-axis micromill controlled by an in-house developed virtual/real-time open computer numerical controlled (CNC) system.

Kinematics and dynamics of a six-degree-of-freedom parallel manipulator with revolute legs

Robotica ◽  
1997 ◽  
Vol 15 (4) ◽  
pp. 385-394 ◽  
Author(s):  
Kourosh E. Zanganeh ◽  
Rosario Sinatra ◽  
Jorge Angeles
Keyword(s):  
Computer Simulation ◽  
Parallel Manipulator ◽  
Kinematic Model ◽  
Degree Of Freedom ◽  
Displacement Velocity ◽  
Kinematics And Dynamics ◽  
Cartesian Space ◽  
Moving Platforms ◽  
Proposed Model ◽  
Six Degree Of Freedom

This paper presents the kinematics and dynamics of a six-degree-of-freedom platform-type parallel manipulator with six revolute legs, i.e. each leg consists of two links that are connected by a revolute joint. Moreover, each leg is connected, in turn, to the base and moving platforms by means of universal and spherical joints, respectively. We first introduce a kinematic model for the manipulator under study. Then, this model is used to derive the kinematics relations of the manipulator at the displacement, velocity and acceleration levels. Based on the proposed model, we develop the dynamics equations of the manipulator using the method of the natural orthogonal complement. The implementation of the model is illustrated by computer simulation and numerical results are presented for a sample trajectory in the Cartesian space.

Determination of the Workspace of 6-DOF Parallel Manipulators

1989 ◽  
Author(s):  
C. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Geometrical Properties ◽  
Cartesian Space ◽  
Six Degree Of Freedom

Abstract This paper presents an algorithm for the determination of the workspace of parallel manipulators. The method described here, which is based on geometrical properties of the workspace, leads to a simple graphical representation of the regions of the three-dimensional Cartesian space that are attainable by the manipulator with a given orientation of the platform. Moreover, the volume of the workspace can be easily computed by performing an integration on its boundary, which is obtained from the algorithm. Examples are included to illustrate the application of the method to a six-degree-of-freedom fully-parallel manipulator.

scholarly journals Path planning optimization of six-degree-of-freedom robotic manipulators using evolutionary algorithms

2020 ◽  
Vol 17 (2) ◽  
pp. 172988142090807
Author(s):  
Sandi Baressi Šegota ◽  
Nikola Anđelić ◽  
Ivan Lorencin ◽  
Milan Saga ◽  
Zlatan Car
Keyword(s):  
Genetic Algorithm ◽  
Simulated Annealing ◽  
Differential Evolution ◽  
Robotic Manipulators ◽  
Robotic Manipulator ◽  
Degree Of Freedom ◽  
Joint Torques ◽  
Point To Point ◽  
Computation Algorithms ◽  
Six Degree Of Freedom

Lowering joint torques of a robotic manipulator enables lowering the energy it uses as well as increase in the longevity of the robotic manipulator. This article proposes the use of evolutionary computation algorithms for optimizing the paths of the robotic manipulator with the goal of lowering the joint torques. The robotic manipulator used for optimization is modelled after a realistic six-degree-of-freedom robotic manipulator. Two cases are observed and these are a single robotic manipulator carrying a weight in a point-to-point trajectory and two robotic manipulators cooperating and moving the same weight along a calculated point-to-point trajectory. The article describes the process used for determining the kinematic properties using Denavit–Hartenberg method and the dynamic equations of the robotic manipulator using Lagrange–Euler and Newton–Euler algorithms. Then, the description of used artificial intelligence optimization algorithms is given – genetic algorithm using random and average recombination, simulated annealing using linear and geometric cooling strategy and differential evolution. The methods are compared and the results show that the genetic algorithm provides best results in regard to torque minimization, with differential evolution also providing comparatively good results and simulated annealing giving the comparatively weakest results while providing smoother torque curves.

Optimal selection of the supporting points of large component aligned and positioned by parallel manipulator

2016 ◽  
Vol 230 (17) ◽  
pp. 3066-3075
Author(s):  
Hongshuang Zhang ◽  
Junxia Jiang ◽  
Yinglin Ke ◽  
Qing Wang
Keyword(s):  
Parallel Manipulator ◽  
Stability Index ◽  
Stiffness Index ◽  
Performance Indices ◽  
Large Component ◽  
Global Performance ◽  
Effective Selection ◽  
Capacity Index ◽  
Six Degree Of Freedom ◽  
Selection Of

Large components such as wing sections should be aligned and positioned in a desired position prior to the final manufacturing or assembly, so a digital alignment and position device based on six degree of freedom parallel manipulator with several prismatic-prismatic-prismatic-spherical branches was designed and fabricated to meet the needs. The digital alignment and position device is an alignment device based on the parallel manipulator, and it is also a positioning and holding fixture for large components manufacturing or assembly. In order to effectively and efficiently select the supporting points of large component where the digital alignment and position device branch is connected with, the performance of the parallel manipulator and the fixture should be comprehensively analyzed at the same time. The global performance indices such as the dexterity index, the bearing capacity index, and the stiffness index are calculated based on the mechanism Jacobean matrix of the parallel manipulator, and the positioning stability index is calculated based on the position Jacobean matrix of the fixture. The results show that the global performance indices are not related to the pose, but the positioning stability index is; in addition, all indices rely on the originally selected supporting points and provide the basis for the effective selection of the supporting points for large component aligned and positioned by the digital alignment and position device, which is based on parallel manipulator with prismatic- prismatic-prismatic-spherical pairs.

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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