Design of Statically Balanced Spatial Mechanisms With Spring Suspensions

2012 ◽  
Vol 4 (2) ◽  
Author(s):  
Po-Yang Lin
Keyword(s):  
Stiffness Matrix ◽  
Computer Software ◽  
Closed Form Solution ◽  
Form Solution ◽  
Static Equilibrium ◽  
Design Parameters ◽  
Gravitational Forces ◽  
Spatial Mechanisms ◽  
Generalized Coordinate ◽  
Loaded Mechanism

This paper proposes a general approach for designing spatial statically balanced mechanisms with articular joints utilizing ideal zero-free-length springs. The proposed statically balanced mechanism can counterbalance the gravitational forces and provides a perfect static equilibrium at any configuration. The method of the paper is based on the energy approach, and a generalized coordinate system is developed to define the configuration of a spatial mechanism and to be a vector basis for the derivation of potential energy. By incorporating the gravitational forces and the spring forces into the system, the stiffness matrix of a spring-loaded mechanism is proposed. The perfect static balance is observed when the stiffness matrix is a diagonal matrix, from which, the design equations can be readily obtained. The closed-form solution of spring design parameters of a statically balanced, spatial, three-articular arm is obtained as a design example. The simulations of the conceptual design are performed by commercial computer software, and the static equilibrium of a quasi-static continuous motion is verified.

Design and Analysis of Automotive Serpentine Belt Drive Systems for Steady State Performance

1997 ◽  
Vol 119 (2) ◽  
pp. 162-168 ◽  
Author(s):  
R. S. Beikmann ◽  
N. C. Perkins ◽  
A. G. Ulsoy
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Design Parameters ◽  
Belt Drive ◽  
Automotive Engine ◽  
Theoretical Predictions ◽  
Serpentine Belt ◽  
Drive Systems

Serpentine belt drive systems with spring-loaded tensioners are now widely used in automotive engine accessory drive design. The steady state tension in each belt span is a major factor affecting belt slip and vibration. These tensions are determined by the accessory loads, the accessory drive geometry, and the tensioner properties. This paper focuses on the design parameters that determine how effectively the tensioner maintains a constant tractive belt tension, despite belt stretch due to accessory loads and belt speed. A nonlinear model predicting the operating state of the belt/tensioner system is derived, and solved using (1) numerical, and (2) approximate, closed-form methods. Inspection of the closed-form solution reveals a single design parameter, referred to as the “tensioner constant,” that measures the effectiveness of the tensioner. Tension measurements on an experimental drive system confirm the theoretical predictions.

A New Accurate Closed-Form Analytical Solution for Junction Temperature of High-Powered Devices

2014 ◽  
Vol 136 (1) ◽  
Author(s):  
J. H. L. Ling ◽  
A. A. O. Tay
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Material Properties ◽  
Heat Dissipation ◽  
Field Effect Transistors ◽  
Closed Form Solution ◽  
Form Solution ◽  
Junction Temperature ◽  
Design Parameters ◽  
Closed Form Analytical Solution

The peak junction temperature has a profound effect on the operational lifetime and performance of high powered microwave devices. Although numerical analysis can help to estimate the peak junction temperature, it can be computationally expensive and time consuming when investigating the effect of the device geometry and material properties on the performance of the device. On the other hand, a closed-form analytical method will allow similar studies to be done easily and quickly. Although some previous analytical solutions have been proposed, the solutions either require over-long computational times or are not so accurate. In this paper, an accurate closed-form analytical solution for the junction temperature of power amplifier field effect transistors (FETs) or monolithic microwave integrated circuits (MMICs) is presented. Its derivation is based on the Green's function integral method on a point heat source developed through the method of images. Unlike most previous works, the location of the heat dissipation region is assumed to be embedded under the gate. Since it is a closed-form solution, the junction temperature as well as the temperature distribution around the gate can be easily calculated. Consequently, the effect of various design parameters and material properties affecting the junction temperature of the device can be easily investigated. This work is also applicable to multifinger devices by employing superposition techniques and has been shown to agree well with both numerical and experimental results.

Closed Form Solutions for Connectivity and Connectivity of Motion in Mechanisms

2000 ◽  
Author(s):  
D. Kohli ◽  
N. Razmara ◽  
A. K. Dhingra
Keyword(s):  
Graph Theory ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Open Chain ◽  
Closed Loops ◽  
Closed Form Solutions ◽  
Spatial Mechanisms ◽  
Special Arrangement

Abstract This paper presents a closed form solution for determining connectivity between any two links in mechanism. The formulation is based on graph theory and its modification. The proposed approach could be applied to both planar and spatial mechanisms including combined planar-spatial mechanisms. Further, the mechanism may have multiple closed loops and/or open-chain substructures. A new concept of Connectivity of Motion has been introduced to determine the connectivity between any two links when the mechanism under consideration has special arrangement of adjacent joints such as joints with parallel and/or intersecting axes. Four examples are presented to illustrate connectivity calculations in spatial mechanisms.

A Parametric Study on Particulate Al-SiC Composite Bolted Joints

2006 ◽  
Author(s):  
Samir N. Shoukry ◽  
Jacky C. Prucz ◽  
Gergis W. William
Keyword(s):  
Load Transfer ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Lap Joints ◽  
Form Solution ◽  
Bolted Joints ◽  
Design Parameters ◽  
Dimensional Finite Element ◽  
Sliding Interfaces ◽  
Three Dimensional Finite Element

The main objective of this study is to predict theoretically the stress distributions around the holes in a bolted joint made of particulate metal matrix composite and to investigate the associated load transfer efficiencies both for a single and double lap bolted joints. A three-dimensional finite element parametric model has been developed to examine the effects of various design parameters on the structural performance of such joints. The main feature of this model is explicit modeling of the sliding interfaces between the connected plates and the washers, and those between the hole and the bolt. The model response showed an excellent agreement with a closed form solution as well as experimental data. The results indicated that unsymmetric configuration of single lap joints causes bending as the load is applied, which is opposite of the double lap joints. This research quantifies the relationship between the stress developed around the hole and washer diameter, tightening pressure, and clearance between the bolt and hole. It was also observed that variations in Young's modulus have no significant effect on the stress concentration around the hole.

Semi-isotropic design of a Stewart platform through constrained optimization

2015 ◽  
Vol 231 (10) ◽  
pp. 1897-1906 ◽  
Author(s):  
Biswajit Halder ◽  
Rana Saha ◽  
Dipankar Sanyal
Keyword(s):  
Constrained Optimization ◽  
Design Optimization ◽  
Translational Motion ◽  
Closed Form Solution ◽  
Positive Definite Function ◽  
Stewart Platform ◽  
Form Solution ◽  
Design Parameters ◽  
Definite Function ◽  
Permissible Range

The isotropic property at home configuration for a semi-regular Stewart platform manipulator with equal leg lengths has been found to be nonachievable by kinematic design optimization study. In this context, a new approach of design optimization has been formulated here for achieving semi-isotropicity through variable transformation that has rendered the constrained optimization over a finite workspace to infinite workspace in the transformed domain. The proposed minimization methodology of a positive definite function for all the angular and translational motion has exhibited strong convergence to zero for values of the design parameters that can be worked out as a closed-form solution only for the cases of linear translation. Finally, the variations of the condition number over the permissible range of all single-degree-of-freedom motions have been carried out. The absence of any other minima in the entire workspace has clearly established the home position as globally optimized.

Dynamic Stresses in a Driven Pile During Installation-Classical Wave Equation Model Solution Using Partial Differential Equations

2014 ◽  
Author(s):  
Syed Muhammad Mohsin Jafri ◽  
Phayak Takkabutr
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Equation ◽  
Closed Form Solution ◽  
Equation Of Motion ◽  
Form Solution ◽  
Design Parameters ◽  
Partial Differential ◽  
Equation Analysis ◽  
Driven Pile

This paper derives and solves the governing dynamic wave equation of motion of a driven pile during the installation phase, when the driven pile is subjected to hammer blows. The pile is assumed as an elastic solid body. The equation of motion is a partial differential equation in space (axial coordinate) and time. The governing partial differential equation of motion is solved for installation boundary conditions, and simplified soil resistance models. The solution of the governing equation yields important design parameters, such as stress variation at any cross-section along the pile length with respect to time, and propagating wave speed. The resulting closed-form solution can be easily implemented using a standard spreadsheet or an engineering calculation program. This approach is compared with conventional wave equation analysis (WEAP) used in industry practice. The conventional wave equation analysis is based on discretization of the pile into mass-spring-damper elements (lumped parameter approach), rather than continuous modeling. The models and solutions from these two approaches are compared.

Closed-Form Steady-State Response Solution of the Twin Rotor Damper and Experimental Validation

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Richard Bäumer ◽  
Uwe Starossek
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Design Parameters ◽  
Control Force ◽  
Steady State Response ◽  
Active Mass ◽  
State Response ◽  
Twin Rotor

In previous research, the twin rotor damper (TRD), an active mass damper, was presented including control algorithms for monofrequent vibrations. In a preferred mode of operation, the continuous rotation mode, two eccentric masses rotate in opposite directions about two parallel axes with a mostly constant angular velocity. The resulting control force is harmonic. Within this paper, the steady-state response of a single-degree-of-freedom (SDOF) oscillator subjected to a harmonic excitation force with and without the TRD is studied. A closed-form solution is presented and validated experimentally. It is shown that the TRD provides damping to the SDOF oscillator until a certain frequency ratio is reached. The provided damping is not only dependent on the design parameters of the TRD but also depends on the steady-state vibration amplitude. The solution serves as a powerful design tool for dimensioning the TRD. The analytical closed-form solution is applicable for other active mass dampers.

An Efficient Method to Generate Element Stiffness Matrix of Quadrilateral Elements in Closed Form on Application of Vehicle Analysis

2016 ◽  
Vol 852 ◽  
pp. 582-587
Author(s):  
P.V. Jeyakarthikeyan ◽  
R. Yogeshwaran ◽  
Karthikk Sridharan
Keyword(s):  
Closed Form ◽  
Stiffness Matrix ◽  
Outer Boundary ◽  
Closed Form Solution ◽  
Simple Calculation ◽  
Field Variable ◽  
Form Solution ◽  
Gauss Quadrature ◽  
Quadrilateral Elements ◽  
Hybrid Grid

This paper presents about generating elemental stiffness matrix for quadrilateral elements in closed form solution method for application on vehicle analysis which is convenient and simple as long as Jacobian is matrix of constant. The interpolation function of the field variable to be found can integrate explicitly once for all, which gives the constant universal matrices A, B and C. Therefore, stiffness matrix is no longer integration of the given functional, it is simple calculation of universal matrices and local co-ordinates of the element. So time taken for generation of element stiffness can be reduced considerably compared to Gauss numerical integration method. For effective use of quadrilateral elements hybrid grid generation is recommended that contains all interior element edges are parallel to each other (rectangle or square elements) and outer boundary elements are quadrilaterals with distortion. So in the Proposed method, the closed form and Gauss numerical method is used explicitly for interior elements and outer elements respectively. The time efficiency of proposed method is compared with conventional Gauss quadrature that is used for entire domain. It is found that the proposed method is much efficient than Gauss Quadrature.

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