General Equations of a Helical Spring With a Cup Damper and Static Verification

1997 ◽  
Vol 119 (2) ◽  
pp. 319-326 ◽  
Author(s):  
Ming Hsun Wu ◽  
Jing Yuan Ho ◽  
Wensyang Hsu
Keyword(s):  
Experimental Data ◽  
Pitch Angle ◽  
Equations Of Motion ◽  
Maximum Error ◽  
Dynamic Equations ◽  
Helical Spring ◽  
Static Force ◽  
Static Verification ◽  
Simulation Results ◽  
Force Displacement

In this study, we derive the general equations of motion for the helical spring with a cup damper by considering the damper’s dilation and varying pitch angle of the helical spring. These dynamic equations are simplified to correlate with previous models. The static force-displacement relation is also derived. The extra stiffness due to the damper’s dilation considered in the force-displacement relation is the first such modeling in this area. In addition, a method is presented to predict the compressing spring’s coil close length and is then verified by experimental data. Moreover, the simulation results of the static force-displacement relation are found to correspond to the experimental data. The maximum error is around 0.6 percent.

General Equations of a Helical Spring With a Cup Damper and Static Verification

1996 ◽  
Author(s):  
Ming Hsun Wu ◽  
Jing Yuan Ho ◽  
Wensyang Hsu
Keyword(s):  
Pitch Angle ◽  
Equations Of Motion ◽  
Static Solution ◽  
Helical Spring ◽  
Static Force ◽  
Experiment Data ◽  
Static Verification ◽  
Solution Of Equations ◽  
Simulation Results ◽  
Force Displacement

Abstract The general equations of motion of the helical spring with a cup damper are derived by considering the dilation of the damper and varying pitch angle of the helical spring. These dynamic equations are simplified to show to agree with other models proposed by previous investigators. The static solution of equations and the static force-displacement relation are also derived. The extra stiffness due to the damper dilation considered in the force-displacement relation is the first such modeling in this area. A method to predict the coil clash length in compressing spring is present and verified with experimental data. Finally, the simulation results of the static force-displacement relation are shown to agree with the experiment data well.

Optimal Stabling of Attitude Maneuver for a Special Satellite With Reaction Wheel Actuators

2010 ◽  
Author(s):  
Seyed Hasan Miri Roknabadi ◽  
Mohamad Fakhari Mehrjardi ◽  
Mehran Mirshams
Keyword(s):  
Attitude Control ◽  
Equations Of Motion ◽  
Low Energy ◽  
Dynamic Equations ◽  
Satellite Motion ◽  
Reaction Wheel ◽  
State Equations ◽  
Time Consumption ◽  
Attitude Maneuver ◽  
Simulation Results

This paper presents an optimal attitude maneuver by Reaction Wheels to achieve desired attitude for a Satellite. At first, Dynamic Equations of motion for a satellite with just three Reaction Wheels of its active actuators are educed, and then State Equations of this system are obtained. An optimal attitude control with the LQR method has exerted for a distinct satellite by its Reaction Wheels. As a result simulation has presented an optimal effort by calculated Gain matrix to achieve desired attitude for chosen Satellite. It shows that satellite becomes stable in desired attitude with a low energy and time consumption. Furthermore equations derivation, coupling of electrical Reaction Wheel equations with dynamic equations of satellite motion, linearizes them and Reaction wheel saturation avoidance approaches are innovative. Simulation results, accuracy of achieving desired attitude and satellite stability support this statement.

Optimal Control of an Assisted Passive Snake-Like Robot Using Feedback Linearization

2007 ◽  
Author(s):  
Saman Mohammadi ◽  
Zoya Heidari ◽  
Hojjat Pendar ◽  
Aria Alasty ◽  
Gholamreza Vossoughi
Keyword(s):  
Optimal Control ◽  
Nonlinear System ◽  
Nonlinear Control ◽  
Feedback Linearization ◽  
Equations Of Motion ◽  
Dynamic Equations ◽  
Unmodeled Dynamics ◽  
Pd Controller ◽  
Simulation Results ◽  
Distinct Line

In this paper we follow two approaches in optimal nonlinear control of a snake-like robot. After deriving the dynamic equations of motion using Gibbs-Appell method, reducing these equations, and some assumptions, feedbacklinearization method was used to linearize the nonlinear system. The obtained controller is used in simulations to control robot to track a desired line, with minimum required torques. Two goals are desired. First the robot’s head is expected to track a distinct line with a given speed. And next, tracking the serpenoid curve is desired. The simulation results prove the controller efficiency. The robustness of the designed controller is shown by comparing the torques with the required torques using a PD controller. Additionally, although we had model mismatches and unmodeled dynamics in controller part, we achieved the desired goals.

Modeling Triple Friction Pendulum Bearings for Response-History Analysis

2008 ◽  
Vol 24 (4) ◽  
pp. 1011-1028 ◽  
Author(s):  
Daniel M. Fenz ◽  
Michael C. Constantinou
Keyword(s):  
Experimental Data ◽  
Equations Of Motion ◽  
Analysis Software ◽  
History Analysis ◽  
Response History Analysis ◽  
Displacement Behavior ◽  
Direct Numerical Integration ◽  
Friction Pendulum ◽  
Force Displacement ◽  
Comparison With Experimental Data

There are currently no applicable hysteresis rules or nonlinear elements available in structural analysis software that can be used to exactly model triple Friction Pendulum bearings for response-history analysis. Series models composed of existing nonlinear elements are proposed since they can be immediately implemented in currently available analysis software. However, the behavior of the triple Friction Pendulum bearing is not exactly that of a series arrangement of single concave Friction Pendulum bearings—though it is similar. This paper describes how to modify the input parameters of the series model in order to precisely retrace the true force-displacement behavior exhibited by this device. Recommendations are made for modeling in SAP2000 and are illustrated through analysis of a simple seismically isolated structure. The results are confirmed by (a) verifying the force-displacement behavior through comparison with experimental data and (b) verifying the analysis through comparison to the results obtained by direct numerical integration of the equations of motion.

The Differential Geometry of the General Helix as Applied to Mechanical Springs

1988 ◽  
Vol 55 (4) ◽  
pp. 831-836 ◽  
Author(s):  
Yuyi Lin ◽  
Albert P. Pisano
Keyword(s):  
Experimental Data ◽  
Differential Geometry ◽  
Fatigue Life ◽  
Pitch Angle ◽  
Helical Spring ◽  
Variable Pitch ◽  
Helical Springs ◽  
Spring Force ◽  
Variable Helix ◽  
Curvature And Torsion

In order to improve the performance of helical springs, such as increasing the fatigue life and suppressing resonance, variable pitch angle and variable helix radius may be incorporated into the helical spring geometry. Employing the tool of differential geometry, new and complete formulae of curvature, torsion, and spring force are derived. It is shown that these formulae are more general and accurate than Kelvin’s curvature and torsion formulae, than commonly used force formulae (Wahl, 1963). Possible simplifications to the complete formulae and the corresponding errors introduced are both discussed and compared with experimental data.

Euler–Lagrange as Pseudo-metric of the RRT algorithm for optimal-time trajectory of flight simulation model in high-density obstacle environment

Robotica ◽  
2015 ◽  
Vol 35 (5) ◽  
pp. 1138-1156 ◽  
Author(s):  
Mohammad Altaher ◽  
Omaima Nomir
Keyword(s):  
Equations Of Motion ◽  
Flight Simulation ◽  
Dynamic Equations ◽  
Optimal Time ◽  
Holonomic Constraints ◽  
Lagrange Formula ◽  
Path Constraints ◽  
Optimized Model ◽  
Simulation Results ◽  
Path Constraint

SUMMARYThis paper introduces a solution to the problem of steering an aerodynamical system, with non-holonomic constraints superimposed on dynamic equations of motion. The proposed approach is a dimensionality reduction of the Optimal Control Problem (OCP) with heavy path constraints to be solved by Rapidly-Exploring Random Tree (RRT) algorithm. In this research, we formulated and solved the OCP with Euler–Lagrange formula in order to find the optimal-time trajectory. The RRT constructs a non-collision path in static, high-dense obstacle environment (i.e. heavy path constraint). Based on a real-world aircraft model, our simulation results found the collision-free path and gave improvements of time and fuel consumption of the optimized Hamiltonian-based model over the original non-optimized model.

Cooperative parameter estimation of a nonuniform payload by multiple quadrotors

Robotica ◽  
2021 ◽  
pp. 1-20
Author(s):  
Farhad Arab ◽  
Farzad A. Shirazi ◽  
Mohammad Reza Hairi Yazdi
Keyword(s):  
Attitude Control ◽  
Equations Of Motion ◽  
Estimation Algorithm ◽  
Adaptive Controller ◽  
Dynamic Equations ◽  
Physical Parameters ◽  
Constraint Forces ◽  
Outer Loop ◽  
Simulation Results

Abstract Thispaper addresses the problem of carrying an unknown nonuniform payload by multiple quadrotor agents. The load is modeled as a rigid body with unknown weight and position of Center of Gravity (CG) for the agents, and is included in their dynamic equations of motion. The agents and the load are assumed to be connected to each other by taut ropes. The Udwadia–Kalaba equation is used to calculate the constraint forces on the ropes acting on each quadrotor. Inner-loop and outer-loop controllers for quadrotors position and attitude control are presented. For the outer loop, an estimation algorithm based on the invariance and immersion adaptive control is utilized to estimate the unknown physical parameters of the payload including mass and CG position without using multi-axes force/torque sensors. The inner-loop controller employs an adaptive controller. Simulation results, for two and four agents carrying a nonuniform rod and cubic payload, show the effectiveness of the proposed algorithm. A case study is also performed to investigate the effect of quadrotors positioning on flight endurance of the cooperative aerial team carrying a nonuniform payload.

Simulation Study of a Spherical Inverted Pendulum on an Omnidirectional Cart With Holonomic Constraints

2018 ◽  
Author(s):  
Sayani Maity ◽  
Greg R. Luecke
Keyword(s):  
Experimental Data ◽  
Horizontal Plane ◽  
Inverted Pendulum ◽  
Vertical Axis ◽  
Dynamic Equations ◽  
Spherical Pendulum ◽  
Holonomic Constraints ◽  
One Dimensional ◽  
Lqr Controller ◽  
Simulation Results

In this paper we develop the control and stabilization of a spherical jointed inverted pendulum balanced on an omnidirectional cart. The system consists of an omnidirectional cart with mecanum wheels equipped with a spherical inverted pendulum attached at the center of the platform. The inverted pendulum is free to fall in any direction perpendicular to the horizontal plane. The omnidirectional cart has the special ability to move in any direction without changing orientation. It can also rotate around its vertical axis. This balancing platform provides a base with holonomic motion to support and balance the pendulum. In this work, the system has been decoupled into two separate subsystems in the x-z and y-z plane. We develop the system dynamic equations in both vertical planes and design a LQR controller to stabilize the system. Using one-dimensional pendulum experimental data, we validate our controller and extend the approach to stabilize the spherical pendulum in both vertical directions. Simulation results are presented to show the effectiveness of the decoupled system LQR controller in stabilizing the spherical pendulum.

LIQUIDUS THERMO-BAROMETER FOR THE MODELING OF MAGNETITE — MELT EQUILIBRIUM

2018 ◽  
pp. 71-80
Author(s):  
N. S. Aryaeva ◽  
E. V. Koptev-Dvornikov ◽  
D. A. Bychkov
Keyword(s):  
Experimental Data ◽  
Liquidus Temperature ◽  
Vertical Structure ◽  
Maximum Error ◽  
Silicate Melt ◽  
System Of Equations ◽  
Wide Range ◽  
Basaltic Melts ◽  
Multidimensional Statistics

A system of equations of thermobarometer for magnetite-silicate melt equilibrium was obtained by method of multidimensional statistics of 93 experimental data of a magnetite solubility in basaltic melts. Equations reproduce experimental data in a wide range of basalt compositions, temperatures and pressures with small errors. Verification of thermobarometers showed the maximum error in liquidus temperature reproducing does not exceed ±7 °C. The level of cumulative magnetite appearance in the vertical structure of Tsypringa, Kivakka, Burakovsky intrusions predicted with errors from ±10 to ±50 m.

BEHAVIORAL MODEL OF A LINEAR VOLTAGE STABILIZER IN THE SPICE LANGUAGE

2019 ◽  
Author(s):  
Aleksey Malahanov
Keyword(s):  
Experimental Data ◽  
Behavioral Model ◽  
Voltage Stabilizer ◽  
Static Mode ◽  
Technical Description ◽  
Simulation Results ◽  
Chip Manufacturer ◽  
Linear Voltage

A variant of the implementation of the behavioral model of a linear voltage stabilizer in the Spice language is presented. The results of modeling in static mode are presented. The simulation results are compared with experimental data and technical description of the chip manufacturer.

Sign in / Sign up

Export Citation Format

Share Document