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.

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.

scholarly journals A FAST AND EFFICIENT MODEL FOR LEARNING TO REACH

2005 ◽  
Vol 02 (04) ◽  
pp. 391-413 ◽  
Author(s):  
GANGHUA SUN ◽  
BRIAN SCASSELLATI
Keyword(s):  
Real Time ◽  
Humanoid Robot ◽  
Kinematic Model ◽  
Careful Analysis ◽  
High Accuracy ◽  
Optimization Process ◽  
Training Samples ◽  
Forward Kinematic ◽  
Hidden Neurons ◽  
Six Degree Of Freedom

This paper proposes a self-supervised model which enables a humanoid robot to learn to reach to visual targets. Only 400 training samples are used to learn a forward kinematic model of the six degree-of-freedom (DOF) arm. The forward model is represented compactly with just 150 hidden neurons and enables high accuracy reaching in real time. We provide an optimization process for the learning parameters and a careful analysis of reaching errors. An extension of the model is presented to address additional DOFs in the neck. The consistency of the model with physiological and psychological observations is elaborated.

scholarly journals Development of six-degree of freedom strapdown terrestrial INS algorithm

2005 ◽  
Vol 2 (1) ◽  
pp. 155-165
Author(s):  
Baghdad Science Journal
Keyword(s):  
Real Time ◽  
High Speed ◽  
Degree Of Freedom ◽  
The Real ◽  
Six Degree Of Freedom

Many of accurate inertial guided missilc systems need to use more complex mathematical calculations and require a high speed processing to ensure the real-time opreation. This will give rise to the need of developing an effcint

scholarly journals Design of a Measurement System for Six-Degree-of-Freedom Geometric Errors of a Linear Guide of a Machine Tool

Sensors ◽  
2018 ◽  
Vol 19 (1) ◽  
pp. 5 ◽  
Author(s):  
Chien-Sheng Liu ◽  
Jia-Jun Lai ◽  
Yong-Tai Luo
Keyword(s):  
Degree Of Freedom ◽  
Geometric Errors ◽  
Light Path ◽  
Linear Guide ◽  
Positioning Errors ◽  
Speed Up ◽  
Analysis Design ◽  
Six Degree Of Freedom ◽  
Straightness Error ◽  
The Mathematical Model

This paper proposes a system utilizing a Renishaw XL80 positioning error measuring interferometer and sensitivity analysis design to measure six-degree-of-freedom (6 DOF) geometric errors of a machine tool’s linear guide. Each error is characterized by high independence with significantly reduced crosstalk, and error calculations are extremely fast and accurate. Initially, the real light path was simulated using Zemax. Then, Matlab’s skew ray tracing method was used to perform mathematical modeling and ray matching. Each error’s sensitivity to the sensor was then analyzed, and curve fitting was used to simplify and speed up the mathematical model computations. Finally, Solidworks was used to design the set of system modules, bringing the proposed system closer to a product. This system measured actual 6 DOF geometric errors of a machine tool’s linear guide, and a comparison is made with the Renishaw XL-80 interferometer measurements. The resulting pitch, yaw, horizontal straightness, and vertical straightness error deviation ranges are ±0.5 arcsec, ±3.6 arcsec, ±2.1 μm, and ±2.3 μm, respectively. The maximum repeatability deviations for the measured guide’s pitch, yaw, roll, horizontal straightness, vertical straightness, and positioning errors are 0.4 arcsec, 0.2 arcsec, 4.2 arcsec, 1.5 μm, 0.3 μm, and 3 μm, respectively.

A Method for Real-Time Estimating Pose of Large Aircraft Component in Process of Pose Adjustment Based on the Unscented Kalman Filter

2012 ◽  
Vol 442 ◽  
pp. 251-255
Author(s):  
Zheng Ying
Keyword(s):  
Kalman Filter ◽  
Real Time ◽  
Unscented Kalman Filter ◽  
Kinematic Model ◽  
Estimation Method ◽  
Time Estimation ◽  
Measuring Point ◽  
Aircraft Component ◽  
Forward Kinematic ◽  
Large Aircraft

To estimate the pose of large aircraft component in pose adjustment quickly and accurately, a real-time estimation method based on Unscented Kalman filter (UKF) is proposed. Firstly, in the process of the aircraft component adjustment, a rough value of aircraft component’s pose is acquired by using forward kinematic model and the displacement of positioners on real time. Then, position of a measuring point fixed on aircraft component is obtained by a laser tracker. At last, UKF is employed to integrate the previous rough value and the measuring point position for evaluating the accurate pose of aircraft component. Numerical simulation results show that the presented method is achieved easily, calculated fast and high accurate.

Kinematic analysis of an augmented 3-RPSP tripod mechanism with six degrees of freedom for bone reduction surgery

2021 ◽  
pp. 095440622110480
Author(s):  
Sinh Nguyen Phu ◽  
Terence Essomba
Keyword(s):  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Femoral Shaft ◽  
Polynomial Equation ◽  
Velocity Model ◽  
Inverse Kinematic ◽  
Reachable Workspace ◽  
Bone Fragments ◽  
Forward Kinematic ◽  
Six Degree Of Freedom

Robotic-assisted bone reduction surgery consists in using robots to reconnect patients’ bone fragments prior to fracture healing. The goal of this study is to propose a novel augmented 3-RPSP tripod mechanism with six degree of freedom for longitudinal bone reduction surgery. Its inverse kinematic model is studied and its forward kinematic model is solved by establishing the constraint equations, applying Sylvester’s dialytic method and finding the solutions of the resulting polynomial equation. The velocity model is calculated and its Jacobian matrix is used to identify its singular configurations. In comparison to the Stewart–Gough platform that is a typical mechanism used in this application, the proposed mechanism offers larger reachable workspace which is an important aspect in the femoral shaft bone reduction. A Physiguide and Msc Adams software are used to carry out a simulation of a real femur fracture reduction using the proposed mechanism to validate its suitability. A robotic prototype has been designed and manufactured in order to test its capability of performing diaphyseal femur reduction surgery.

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