Analytical Evaluation of the Double Stewart Platform Tensile Truss Stiffness Matrix

2013 ◽  
Vol 6 (1) ◽  
Author(s):  
Adam H. Hesselroth ◽  
Michael P. Hennessey
Keyword(s):  
Stiffness Matrix ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Stewart Platform ◽  
Physical Models ◽  
Measuring System ◽  
Small Displacement ◽  
Mobile Platforms ◽  
Specific System ◽  
External Forces

The 6 × 6 stiffness matrix for a single Stewart platform tensile truss is well known. This work extends the methodology used to determine the stiffness matrix of a double Stewart platform system, in which one Stewart platform is stacked on top of another, in serial fashion. A double Stewart platform may offer advantages for some applications in terms of increased stiffness in certain directions. Using principles of statics and considering small displacement perturbations in three-dimensional space of both mobile platforms (middle and bottom) from their weighted equilibrium locations, displacements can be related in a linear manner to application loading, implying a stiffness matrix. Scripts are then developed and executed in matlabtm to determine the stiffness matrix of a specific system. The matlabtm result is validated using single and double Stewart platform physical models and measuring system compliance responses to external forces and moments.

Energy Harvesting Aspects of Irregular Vibrating Forces Acting on Piezoelectric Devices

2015 ◽  
pp. 143-158
Author(s):  
Alessandro Massaro
Keyword(s):  
Energy Harvesting ◽  
Piezoelectric Materials ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Output Current ◽  
Vibrating System ◽  
External Forces ◽  
Piezoelectric Devices ◽  
Three Dimensional Space

After a brief introduction of piezoelectric materials, this chapter focuses on the characterization of vibrating freestanding piezoelectric AlN devices forced by different external forces acting simultaneously. The analyzed vibrating forces are applied mainly to piezoelectric freestanding structures stimulated by irregular vibration phenomena. Particular kinds of theoretical noise signals are commented. The goal of the chapter is to analyze the effect of the noise in order to model the chaotic vibrating system and to predict the output current signals. Moreover, the author also shows a possible alternative way to detect different vibrating force directions in the three dimensional space by means of curved piezoelectric layouts.

A Conceptual Design of a Measuring System of Tennis Batting Motion Attitude Based on MEMS Sensors

2012 ◽  
Vol 198-199 ◽  
pp. 1053-1056
Author(s):  
Liang Han ◽  
Jing Song Jin ◽  
Wei Zhang
Keyword(s):  
Measurement System ◽  
Position Control ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Human Movement ◽  
Sports Injury ◽  
Measuring System ◽  
Attitude Measurement ◽  
Instructional Role ◽  
System Composition

Tennis is a very elegant sport, with a strong sense of competitiveness and appreciation, which has gained more and more attentions in our country, and it tends to be a fashion. This project is to achieve the measurement of tennis batting motion attitude in three dimensional space using a combination of the three-axis MEMS(Micro-electromechanical Systems) sensors, and make research on the principle of measurement system, composition and data acquisition. Body posture measurement system is to measure the attitude measurement in human movement, it can be applied to study the movement posture or to meet the requirements of position control, which provides theoretical foundation for scientific training and prevention of sports injury and also plays a significant and instructional role in improving the training levels of tennis playing and generalizing nationwide fitness campaign.

Dynamical Simulation of a Knotless Netting Based on Explicit Method

2012 ◽  
Vol 235 ◽  
pp. 210-215
Author(s):  
Cheng Zhou ◽  
Liu Xiong Xu ◽  
Xin Feng Zhang ◽  
Guo Ping Zhu
Keyword(s):  
Sea Water ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Euler Method ◽  
Physical Models ◽  
Element Analysis ◽  
Dynamical Simulation ◽  
Tensile Forces ◽  
Spring System ◽  
Mass Spring

Based on finite element analysis and explicit Euler method, the present study visualized the dynamical simulation of a knotless netting in R environment. In the physical models, the linking between knot and twine were considered as a mass-spring system. Vector algebra methods were applied to analyze the hydrodynamic forces and tensile forces of the spring. To solve the equations numerically, explicit Euler method was introduced for the mechanical system to achieve the stable solutions. A package of scatterplot3d in R program was transferred to realize the visualization of the knotless netting in three-dimensional space. The results of dynamical simulation were displayed distinctly to show the sinking processes and equibibrium state of the knotless netting in the sea water.

scholarly journals The system of acquisition and archiving of motion parameters of mobile systems - an overview of measuring sensors

2019 ◽  
Vol 20 (1-2) ◽  
pp. 234-240
Author(s):  
Jakub Grabiński ◽  
Konrad Waluś
Keyword(s):  
Coordinate System ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Mobile Systems ◽  
Measuring System ◽  
Starting Point ◽  
Macro Scale ◽  
Mems Technology ◽  
Motion Parameters ◽  
Cartesian Coordinate

As part of the work, a measuring system is presented that allows collecting and recording vehicle motion parameters. To build the system, an inertial navigation module was used, consisting of two-axis accelerometers and gyroscopes made in MEMS technology. The tests were carried out and calculation methods were developed to allow the collected data to be referenced, to a point in the three-dimensional space, in order to determine the trajectory of the vehicle's movement. The built-in measuring system uses three types of sensors: accelerometer, gyroscope, magnetometer. Each of these sensors allows the measurement of the physical size in three orthogonal axes of the Cartesian coordinate system. In addition, the work uses a satellite navigation module (GPS), as a reference on the "macro" scale (coordinate system related to the center of the globe with a radius of about 6371 km) for the inertial updating module (INS / IMU), enabling accurate measurement in the "micro" scale (the coordinate system associated with the starting point of the traffic for the route, the length of which does not exceed several hundred meters). The article presents an overview of available measuring sensors with special consideration of the parameters of selected sensors and errors introduced into the measurement system.

A Three-Dimensional Numerical Model for Simulating Deformation and Failure of Blocky Rock Structures

2006 ◽  
Vol 306-308 ◽  
pp. 1391-1396 ◽  
Author(s):  
Yu Yong Jiao ◽  
Quan Sheng Liu ◽  
Shu Cai Li
Keyword(s):  
Numerical Model ◽  
Stiffness Matrix ◽  
Three Dimensional ◽  
Small Displacement ◽  
Equilibrium Equations ◽  
Deformation And Failure ◽  
Static Relaxation ◽  
Global Equilibrium ◽  
C Program ◽  
Global Stiffness Matrix

This paper presents a three-dimensional numerical model for simulation of blocky rock structures based on static relaxation approach. The proposed method utilizes static equilibrium equations to calculate the displacements of blocks, compared to Newton’s second law applied by the traditional DEM. In order to obtain displacements simultaneously, the technique of global stiffness matrix is introduced in to form the global equilibrium equations. Because large displacements come from the accumulation of small displacement increments, an iteration procedure is adopted in the calculation. A C++ program is developed based on the proposed algorithm, and an illustrative example is computed for verification.

The Geometrical Mode Analysis of a Vibrating System With the Planes of Symmetry

1999 ◽  
Author(s):  
Byung Ju Dan ◽  
Yong Je Choi
Keyword(s):  
Stiffness Matrix ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Mode Analysis ◽  
Vibration Modes ◽  
Pure Rotation ◽  
Parallel Axis ◽  
Congruence Transformation ◽  
Disc Drive ◽  
Three Dimensional Space

Abstract Vibration modes obtained from a modal analysis can be better explained from a screw theoretical standpoint. A vibration mode can be geometrically interpreted as a pure rotation about the vibration center in a plane and as a twisting motion on a screw in a three dimensional space. This paper presents a method to diagonalize a spatial stiffness matrix by use of a parallel axis congruence transformation when the stiffness matrix satisfies some conditions. It also describes that the diagonalized stiffness matrix can have the planes of symmetry depending on the location of the center of elasticity. For a system with the planes of symmetry, the vibration modes can be expressed by the axes of vibration. Analytical solutions for the axes of vibration have been derived. A numerical example of an application to the vibration analysis of an optical disc drive has been presented.

Stresses in equilibrium configurations of inextensible nets with slack

2015 ◽  
Vol 22 (4) ◽  
pp. 649-665 ◽  
Author(s):  
Miroslav Šilhavý
Keyword(s):  
Dimensional Space ◽  
Minimum Energy ◽  
Three Dimensional ◽  
Deformation Energy ◽  
Equality Sign ◽  
Stress Concentrations ◽  
Equilibrium Configurations ◽  
Present Context ◽  
External Forces ◽  
Additive Measures

The paper deals with nets formed by two families of fibers (cords) which can grow shorter but not longer, in a deformation. The nets are treated as two-dimensional continua in the three-dimensional space. The inextensibility condition places unilateral constraint on the partial derivatives y,1 and y,2 of the deformation [Formula: see text] of the form [Formula: see text] [Formula: see text] There is no deformation energy, the total energy reduces to the potential energy of the net under external forces. Equilibrium configurations are those of minimum energy. The stresses in equilibrium configurations thus reduce to the reactions to the constraints. Nonzero stresses occur only in tense regions where one or two constraints are satisfied with the equality sign. The paper follows the work of Paroni in treating the stress problem via the dual variational problem in the sense of convex analysis. Unlike in the work of Paroni, where stresses are modeled as finitely additive set functions, here a (perhaps more economic) choice of spaces is made that leads to more accessible stresses represented by (countably additive) measures. The present development is made possible by an observation, of independent value, that the space of measures with divergence measure is the dual of another Banach space, in the present context naturally interpreted as the space of strains. Our measures generalize stress fields represented by ordinary functions to account for stress concentrations along folded lines in tension, frequently occurring in equilibrium configurations of the net.

A Finite Element Formulation for the Dynamic Analysis of Machine Components Fabricated From Composite Materials

1992 ◽  
Author(s):  
A. Semos ◽  
C. Chassapis
Keyword(s):  
Finite Element ◽  
Composite Materials ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Element Formulation ◽  
Reinforced Composite ◽  
External Forces ◽  
Three Dimensional Space

Abstract In this paper finite element procedures are presented for analyzing the elastic-dynamic behavior of mechanical components fabricated from fiber-reinforced composite materials. An arbitrarily laminated composite plate element is created which allows the analysis of components that are moving in three dimensional space. The five D.O.F. per node static model of S. C. Panda and R. Natarajan is used as a basis for the derivation of the dynamic model. The elemental equations of motion are derived from Hamilton’s Principle. The formulation considers the total kinetic and strain energies of the moving element, together with the work due to bending, caused by the transversely acting external forces, as well as that due to the foreshortening of the element, caused by axially applied loads.

Workspace Analysis of Closed Loop Mechanisms With Unilateral Constraints

1989 ◽  
Author(s):  
D.-Y. Jo ◽  
E. J. Haug
Keyword(s):  
Numerical Methods ◽  
Closed Loop ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Inequality Constraints ◽  
Stewart Platform ◽  
Unilateral Constraints ◽  
Higher Dimensional ◽  
Workspace Analysis ◽  
Slack Variable

Abstract Kinematics of mechanisms that contain elements with unilateral constraints such as stops are characterized by systems of equalities and inequalities. A slack variable formulation is introduced to convert inequality constraints to equalities, in a higher dimensional space of variables. The slack variable formulation permits use of manifold based theoretical and numerical methods for analysis of the boundaries of workspaces. The workspace of a simplified Stewart platform is analyzed, including rotatability of the top platform. Sets of reachable points of the top platform of a three dimensional Stewart platform, with fixed platform orientation, are analyzed.

Analysis of a gyroscopic force measuring system in three-dimensional space

Measurement ◽  
2000 ◽  
Vol 28 (4) ◽  
pp. 235-247 ◽  
Author(s):  
M. Kasahara ◽  
S. Kurosu ◽  
M. Adachi ◽  
K. Kamimura
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Measuring System ◽  
Gyroscopic Force ◽  
Three Dimensional Space
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