Inverse Static Analysis for a Planar Compliant Platform Mechanism

2004 ◽  
Author(s):  
Hai-Jun Su ◽  
J. Michael McCarthy
Keyword(s):  
Potential Energy ◽  
Static Analysis ◽  
Parallel Mechanism ◽  
Equilibrium Points ◽  
Potential Energy Function ◽  
System Behavior ◽  
Equilibrium Conditions ◽  
Equilibrium Configurations ◽  
Moving Platform ◽  
Derivatives Of

This paper studies the inverse static analysis of a planar parallel mechanism with compliant limbs. A known force and moment is applied to the moving platform, and it is required to determine the assembly configurations, or equilibrium points. Partial derivatives of the potential energy function yields the equilibrium conditions. The geometric and static constraints lead to a system of ten polynomials with ten unknowns. We use polynomial homotopy method to find that there are as many as 70 equilibrium configurations. Two examples with equilateral geometry are provided. We also examine the system behavior during a movement between selected equilibrium positions.

A Polynomial Homotopy Formulation of the Inverse Static Analysis of Planar Compliant Mechanisms

2005 ◽  
Vol 128 (4) ◽  
pp. 776-786 ◽  
Author(s):  
Hai-Jun Su ◽  
J. Michael McCarthy
Keyword(s):  
Potential Energy ◽  
Static Analysis ◽  
Compliant Mechanisms ◽  
Potential Energy Function ◽  
Equilibrium Equations ◽  
Equilibrium Configurations ◽  
Force Moment ◽  
Four Bar Linkage ◽  
Derivatives Of ◽  
Raphson Iteration

This paper formulates the inverse static analysis of planar compliant mechanisms in polynomial form. The goal is to find the equilibrium configurations of the system in response to a known force/moment applied to the mechanism. The geometric constraint of the linkage defines a set of kinematics equations which are combined with equilibrium equations obtained from partial derivatives of the potential-energy function. In order to apply polynomial homotopy solver to these equations, we approximate the linear torsion spring torque at each joint by using sine and cosine functions. The results obtained from the homotopy solver are then refined using Newton-Raphson iteration. To demonstrate the analysis steps, we study two example planar compliant mechanisms, a four-bar linkage with two torsional springs, and a parallel platform supported by three linear springs. Numerical examples are provided together with plots of the potential energy during a movement between selected equilibrium positions.

Configuration Optimization and Static Analysis of Adjusting Parallel Mechanism for the Sub-Reflector of Antenna

2011 ◽  
Vol 338 ◽  
pp. 425-430 ◽  
Author(s):  
Yu Lei Hou ◽  
Yan Bin Duan ◽  
Jian Tao Yao ◽  
Da Xing Zeng ◽  
Yong Sheng Zhao
Keyword(s):  
Real Time ◽  
Static Analysis ◽  
Structural Design ◽  
External Load ◽  
Parallel Mechanism ◽  
Structural Parameters ◽  
Configuration Optimization ◽  
Theoretical Significance ◽  
Moving Platform ◽  
Minimum Force

For the real-time pose adjustment of the sub-reflector of antenna to ensure its best condition, Stewart platform-based mechanism is adopted. This paper presents the configuration optimization of the adjusting parallel mechanism taking the minimum force acted on each limb as the target, and the basic structural parameters of the mechanism are obtained. Considering the weight of the moving platform, the external load, and the influence of the snow and the wind, the maximum force acted on the limbs of the mechanism in the required workspace is calculated, which established the foundation for the structural design of the mechanism. The contents of this paper possess theoretical significance and engineering value for the development of the adjusting mechanism for the sub-reflector of antenna.

KINEMATICS AND WORKSPACE ANALYSIS OF A 3 DEGREE OF FREEDOM PARALLEL MECHANISM WITH PARALLELOGRAM LINKAGE

2017 ◽  
Vol 41 (5) ◽  
pp. 922-935
Author(s):  
HongJun San ◽  
JunSong Lei ◽  
JiuPeng Chen ◽  
ZhengMing Xiao ◽  
JunJie Zhao
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Analytical Method ◽  
Theoretical Basis ◽  
Parallel Mechanism ◽  
Graphical Method ◽  
Degree Of Freedom ◽  
Workspace Analysis ◽  
Fixed Base ◽  
Moving Platform

In this paper, a 3-DOF translational parallel mechanism with parallelogram linkage was studied. According to the space vector relation between the moving platform and the fixed base, the direct and inverse position solutions of this mechanism was deduced through analytical method. In addition, the error of the algorithm was analyzed, and the algorithm had turned out to be effective and to have the satisfactory computational precision. On the above basis, the workspace of this mechanism was found through graphical method, which was compared with that of finding through Monte Carlo method, and there was the feasibility for analyzing the workspace of the mechanism by graphical method. The characteristic of the mechanism was analyzed by comparing the results of two analysis methods, which provided a theoretical basis for the application of the mechanism.

Dynamics of a Two-DOF Parallel Pointing Mechanism

2005 ◽  
Author(s):  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Numerical Simulation ◽  
Parallel Mechanism ◽  
Inverse Dynamics ◽  
Kinematic Model ◽  
Degree Of Freedom ◽  
Numerical Examples ◽  
Proposed Model ◽  
Dynamic Analyses ◽  
Moving Platform ◽  
Two Degree Of Freedom

This paper presents kinematic and dynamic analyses of a two-degree-of-freedom pointing parallel mechanism. The mechanism consists of a moving platform, connected to a fixed platform by two legs of type PUS (prismatic-universal-spherical). At first a simplified kinematic model of the pointing mechanism is introduced. Based on this proposed model, the dynamics equations of the system using the Natural Orthogonal Complement method are developed. Numerical examples of the inverse dynamics results are presented by numerical simulation.

PREDICTION OF THE TRANSPORT PROPERTIES OF SF6 WITH O2, CO2, CF4, N2 AND CH4 MIXTURES AT LOW DENSITY BY THE INVERSION METHOD (PART II)

2004 ◽  
Vol 03 (01) ◽  
pp. 69-90 ◽  
Author(s):  
BEHZAD HAGHIGHI ◽  
ALIREZA HASSANI DJAVANMARDI ◽  
MOHAMAD MEHDI PAPARI ◽  
MOHSEN NAJAFI
Keyword(s):  
Potential Energy ◽  
Diffusion Coefficients ◽  
Potential Energy Function ◽  
Model Potential ◽  
Inversion Method ◽  
Low Density ◽  
Initial Model ◽  
Lennard Jones ◽  
Inversion Procedure ◽  
And Diffusion

Viscosity and diffusion coefficients for five equimolar binary gas mixtures of SF 6 with O 2, CO 2, CF 4, N 2 and CH 4 gases are determined from the extended principle of corresponding states of viscosity by the inversion technique. The Lennard–Jones 12-6 (LJ 12-6) potential energy function is used as the initial model potential required by the technique. The obtained interaction potential energies from the inversion procedure reproduce viscosity within 1% and diffusion coefficients within 5%.

The Parallel Mechanism and Variable Acceleration Control Method

2013 ◽  
Vol 579-580 ◽  
pp. 659-664
Author(s):  
Xiang Bo Ouyang ◽  
Ke Tian Li ◽  
Hong Jian Xia ◽  
Su Juan Wang ◽  
Huan Wei Zhou ◽  
...  
Keyword(s):  
Parallel Mechanism ◽  
Control Method ◽  
The Other ◽  
Connecting Rod ◽  
Motion Platform ◽  
The Third ◽  
Symmetric Structure ◽  
Slide Block ◽  
Operation Process ◽  
Moving Platform

t presents the parallel mechanism and variable acceleration control method, which is composed of slider, connecting rod, moving platform and linear guide etc. The motion platform is supported by three connecting rods through hinging, the other end of the connecting rods are respectively hinged with two sliders. Among them two pairs of connecting rod, two sliders and the moving platform formed a symmetric structure that is the so called Parallel Mechanism. The third connecting rod is parallel to one of two connecting rods, so that the two parallel connecting rods, slide block and the moving platform formed a parallelogram structure, it makes that the moving platform is always parallel to liner guiderail in the process of movement. By controlling the two sliders moving in the way of variable acceleration, it can make the trajectory curve, speed curve and acceleration curve of the moving platform are continuous, smooth, so impact and vibration of the moving platform is limited in the operation process.

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