Analysis of Mechanical Error’s Effect on the Measurement Accuracy of the Six-Axis Force Sensor

2014 ◽  
Vol 627 ◽  
pp. 177-181
Author(s):  
Ru Nan Liang
Keyword(s):  
Mathematical Model ◽  
Monte Carlo ◽  
Theoretical Basis ◽  
Measurement Accuracy ◽  
Force Sensor ◽  
Stewart Platform ◽  
System Structure ◽  
The Monte Carlo Method ◽  
Six Degree Of Freedom ◽  
The Mathematical Model

Force sensor based on the six degree of freedom (6-DoF) Stewart platform is universal for wide applications. Mechanism errors are significant for its measuring accuracy. However, because of the multi-variables and the complicated forms, it is difficult to solve the expression directly. The Monte Carlo method is proposed based on the analysis of the system structure and the mathematical model. The effect of mechanism errors on the measurement accuracy was assessed. With this method, a complex accuracy expression of the sensor could be avoided. It also provided a theoretical basis for designing the sensor of the Stewart platform.

scholarly journals Study on the Mathematical Model of Vacuum Breaker Valve for Large Air Mass Conditions

Water ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 1358
Author(s):  
Zhang ◽  
Fan ◽  
Yu ◽  
Zhang ◽  
Lv ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Theoretical Basis ◽  
Isothermal Process ◽  
Air Mass ◽  
Protection Scheme ◽  
Calculation Results ◽  
Air Valve ◽  
The Mathematical Model ◽  
Valve Model ◽  
Derivation Process

The mathematical model of vacuum breaker valve is significant to the protection scheme. The more accurate the vacuum breaker valve model, the more reliable the calculation results. In this study, the application conditions of the air valve model are analyzed according to the assumptions used in the derivation, and the contradictions between these assumptions are proposed. Then, according to the different working characteristics between the vacuum breaker valve on the siphon outlet pipe and the air valve, the vacuum breaker valve model is deduced based on the modified assumptions. In the derivation process, the thermodynamic change of the gas in the vacuum breaker valve is assumed to follow the isentropic process rather than an isothermal process, and the water level in the vacuum breaker valve is considered to be changeable. An engineering case is introduced, and the results calculated according to the vacuum breaker valve model are compared with those resulting from the air valve model. The results indicate that the vacuum breaker valve model is suitable for large air mass conditions and can provide a theoretical basis for the numerical simulation and settings of vacuum breaker valves.

scholarly journals An Improved Capacitive Sensor for Detecting the Micro-Clearance of Spherical Joints

Sensors ◽  
2019 ◽  
Vol 19 (12) ◽  
pp. 2694 ◽  
Author(s):  
Wen Wang ◽  
Wenjun Qiu ◽  
He Yang ◽  
Haimei Wu ◽  
Guang Shi ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Real Time ◽  
Measurement Accuracy ◽  
Detection Method ◽  
Capacitive Sensor ◽  
Parallel Manipulators ◽  
Differential Capacitance ◽  
Industrial Robots ◽  
The Mathematical Model ◽  
Fringe Effect

Due to the flexible and compact structures, spherical joints are widely used in parallel manipulators and industrial robots. Real-time detection of the clearance between the ball and the socket in spherical joints is beneficial to compensate motion errors of mechanical systems and improve their transmission accuracy. This work proposes an improved capacitive sensor for detecting the micro-clearance of spherical joints. First, the structure of the capacitive sensor is proposed. Then, the mathematical model for the differential capacitance of the sensor and the eccentric micro-displacement of the ball is deduced. Finally, the capacitance values of the capacitive sensor are simulated with Ansoft Maxwell. The simulated values of the differential capacitances at different eccentric displacements agree well with the theoretical ones, indicating the feasibility of the proposed detection method. In addition, the simulated results show that the proposed capacitive sensor could effectively reduce the capacitive fringe effect, improving the measurement accuracy.

Research and Design of a Pre-Stressed Six-Component Force/Torque Sensor Based on the Stewart Platform

2005 ◽  
Author(s):  
Yong-Sheng Zhao ◽  
Yu-Lei Hou ◽  
Zhi-Wei Yan ◽  
Hui-Ling Yuan ◽  
Jin Gao
Keyword(s):  
Mathematical Model ◽  
Screw Theory ◽  
Parallel Architecture ◽  
Stewart Platform ◽  
Influence Coefficient ◽  
Torque Sensor ◽  
Static Calibration ◽  
The Mathematical Model ◽  
Research And Design ◽  
Component Force

This paper presents the research and design of a novel parallel architecture of pre-stressed six-component force/torque sensor based on the Stewart platform. The mathematical model of the structure was build by using the screw theory. The influence of joint frictional moment on the performances of the sensor is analyzed by using the concept of kinematic influence coefficient. In this paper, we define the indices of force/torque isotropy and generalized amplifying index to evaluate the performances of the sensor and discuss the optimal design of the sensor dimensions considering these indices. The prototype sensor was designed and manufactured. The theoretical and experimental study of the static calibration of the prototype is carried out, and the problem of the hyperstatic is solved perfectly. The results from the static calibration experimentation validate the correctness of the theoretical analysis.

scholarly journals Research on Mathematical Model for Non-Uniformly Qualitative Suspension Cable

2018 ◽  
Vol 175 ◽  
pp. 03039
Author(s):  
Hu Yong ◽  
Du Yuxin ◽  
Cao Yong ◽  
Wang MaoSen ◽  
Ma Yuchi ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Perturbation Method ◽  
Radio Telescope ◽  
Theoretical Basis ◽  
Transcendental Function ◽  
Concentrated Loads ◽  
Real Situation ◽  
The Real ◽  
Suspension Cable ◽  
The Mathematical Model

Catenary theory is recognized as the most effective suspension theory which can reflect the real situation of suspension. Catenary equation belongs to transcendental function, so there are some difficulties in calculation and application. Parabola theory, suspension curve theory and perturbation method are gradually formed as the theoretical basis for the study of suspension cables. This paper takes the 500m spherical radio telescope project as the background. The modeling method of suspension cable under multiple concentrated loads is analyzed, and the mathematical model of supporting cable after load is derived. The research in this paper provides a reference for the establishment of mathematical model of suspension cable in practice.

Dynamic analysis of Hexarot: axis-symmetric parallel manipulator

Robotica ◽  
2017 ◽  
Vol 36 (2) ◽  
pp. 225-240 ◽  
Author(s):  
Siamak Pedrammehr ◽  
Behzad Danaei ◽  
Hamid Abdi ◽  
Mehdi Tale Masouleh ◽  
Saeid Nahavandi
Keyword(s):  
Mathematical Model ◽  
Parallel Manipulator ◽  
Dynamic Models ◽  
Inverse Kinematic ◽  
Inverse Kinematic Problem ◽  
Euler Approach ◽  
Six Degree Of Freedom ◽  
The Mathematical Model ◽  
Actuated Joints ◽  
Good Agreement

SUMMARYIn this study, the kinematics and dynamics of a six-degree-of-freedom parallel manipulator, known as Hexarot, are evaluated. Hexarot is classified under axis-symmetric robotic mechanisms. The manipulator comprises a cylindrical base column and six actuated upper arms, which are connected to a platform through passive joints and six lower arms. The actuators of the mechanism are located inside a cylindrical-shaped base, which allows the mechanism to rotate infinitely about the axes of the latter column. In the context of kinematics, the inverse-kinematic problem is solved using positions, velocities, and accelerations of the actuated joints with respect to the position, orientation, and motion of the platform. Accordingly, the main objective of this study is to dynamically model the manipulator using the Newton–Euler approach. For validation, the obtained dynamic model of the Hexarot manipulator is simulated in MATLAB based on the formulations presented in this paper. The kinematic and dynamic models of the manipulator are simulated for a given motion scenario using MATLAB and ADAMS. The results of the mathematical model obtained using MATLAB are in good agreement with that using the ADAMS model, confirming the effectiveness of the proposed mathematical model.

scholarly journals Regression Monte Carlo for microgrid management

2019 ◽  
Vol 65 ◽  
pp. 46-67
Author(s):  
Clemence Alasseur ◽  
Alessandro Balata ◽  
Sahar Ben Aziza ◽  
Aditya Maheshwari ◽  
Peter Tankov ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Monte Carlo ◽  
Storage System ◽  
Management Problem ◽  
Diesel Generator ◽  
High Demand ◽  
Photovoltaic Panels ◽  
Monte Carlo Algorithms ◽  
Islanded Microgrid ◽  
The Mathematical Model

We study an islanded microgrid system designed to supply a small village with the power produced by photovoltaic panels, wind turbines and a diesel generator. A battery storage system device is used to shift power from times of high renewable production to times of high demand. We build on the mathematical model introduced in [14] and optimize the diesel consumption under a “no-blackout” constraint. We introduce a methodology to solve microgrid management problem using different variants of Regression Monte Carlo algorithms and use numerical simulations to infer results about the optimal design of the grid.

Research on the Mathematical Model of the Plastic Profile Cooling Analysis

2012 ◽  
Vol 164 ◽  
pp. 214-217
Author(s):  
Xiang Shan Huang ◽  
Li Dan Chen
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Thermal Analysis ◽  
Reynolds Number ◽  
Theoretical Basis ◽  
Flow State ◽  
Function Blocks ◽  
Plastic Profile ◽  
The Mathematical Model ◽  
Fluid Parameters

According to the assumption of the plastic profile cooling analysis, Prandtl number Pr and Reynolds number Re can be derived from the fluid parameters. The paper judge and analyze the movement of flow state, further study the formula of heat transfer coefficient α, thermal analysis and boundary conditions in Reynolds number Re. The experimental results show mathematical model, which provides a theoretical basis for the cooling and forming of function blocks, it has certain guiding significance.

Research and Design of Pneumatic AMT Actuator

2011 ◽  
Vol 52-54 ◽  
pp. 318-323
Author(s):  
Jian Zhong Wang ◽  
Liang Chu ◽  
Xin Tian Lu
Keyword(s):  
Mathematical Model ◽  
Dynamic Model ◽  
Theoretical Basis ◽  
Structure Characteristics ◽  
Design Scheme ◽  
Heavy Truck ◽  
The Mathematical Model ◽  
Research And Design

According to the design requests of certain heavy truck, this paper introduces a design scheme of pneumatic AMT automatic shift system, which focuses on the structure characteristics and working principles of the three-position cylinder controlled by two solenoid valves. And the mathematical model of the three-position cylinder controlled by two solenoid valves is established based on pneumatic principle. The dynamic model of this mechanism was built by AMEsim software. The variety of pressure and stroke of intake/exhaust chamber was simulated under different air pressures. The theoretical basis is provided to design the AMT election-shift actuator.

Mathematical Model and Error Analysis of Coordinate Measuring Arm with Revo Revolving Body

2011 ◽  
Vol 52-54 ◽  
pp. 156-161 ◽  
Author(s):  
Lei Zhao ◽  
Shu Gui Liu
Keyword(s):  
Mathematical Model ◽  
Measurement Accuracy ◽  
System Model ◽  
Error Sources ◽  
Spherical Domain ◽  
New Type ◽  
Space Coordinate ◽  
Improving Accuracy ◽  
Revolving Body ◽  
The Mathematical Model

A new type of coordinate measuring arm with a Revo revolving body which can realize quick measuring in spherical domain has high stability, fast measuring speed and high accuracy compared with common coordinate measuring arm. We use the method of space coordinate transformation to solve the problem that the transformation matrix can’t be got from Revo body to test head by DH method, and apply DH theory to build the mathematical model of system. The system model is verified right by sketching. The error model is built and the effect of measurement accuracy from all error sources is deeply analyzed. It presents a theory foundation for further researching on improving accuracy of this new type of coordinate measuring arm.

scholarly journals Characterization and Correction of the Geometric Errors using a Confocal Microscope for Extended Topography Measurement, Part II: Experimental Study and Uncertainty Evaluation

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1217 ◽  
Author(s):  
Wang ◽  
Gómez ◽  
Yu
Keyword(s):  
Mathematical Model ◽  
Measurement Data ◽  
Confocal Microscope ◽  
Geometric Errors ◽  
Data Partition ◽  
The Monte Carlo Method ◽  
Measurement Results ◽  
The Mean ◽  
The Mathematical Model ◽  
Certified Values

This paper presents the experimental implementations of the mathematical models and algorithms developed in Part I. Two experiments are carried out. The first experiment determines the correction coefficients of the mathematical model. The dot grid target is measured, and the measurement data are processed by our developed and validated algorithms introduced in Part I. The values of the coefficients are indicated and analyzed. Uncertainties are evaluated using the Monte Carlo method. The second experiment measures a different area of the dot grid target. The measurement results are corrected according to the coefficients determined in the first experiment. The mean residual between the measured points and their corresponding certified values reduced 29.6% after the correction. The sum of squared errors reduced 47.7%. The methods and the algorithms for raw data processing, such as data partition, fittings of dots’ centers, K-means clustering, etc., are the same for the two experiments. The experimental results demonstrate that our method for the correction of the errors produced by the movement of the lateral stage of a confocal microscope is meaningful and practicable.

Sign in / Sign up

Export Citation Format

Share Document