Symbolic Formulation of a Path-Following Joint for Multibody Dynamics

2014 ◽  
Author(s):  
Andrew Hall ◽  
Chad Schmitke ◽  
John McPhee
Keyword(s):  
Path Length ◽  
Closed Form Solution ◽  
Path Following ◽  
Form Solution ◽  
Circular Path ◽  
Multibody Modeling ◽  
Graph Theoretic ◽  
Suspension Systems ◽  
Spline Fitting ◽  
Definition Of

We present a specialized multibody joint that constrains motion to a spatial path. The joint is used in the reduction of 1 degree-of-freedom systems with complex kinematics. Example applications of the joint are: the reduction of vehicle suspension systems, or the representation of biological joints. The new joint is implemented in the graph-theoretic symbolic multibody modeling environment of MapleSim and is formulated in such a way that a single ordinary differential equation is used to describe the resulting kinematic pair. A particle moving along a planar semi-circular path was chosen as the first example for successful validation of the new joint since a simple closed-form solution in terms of the path length exists. To represent arbitrary curves, the path must first be parameterized in terms of its path length. Next, a differentiable mathematical definition of the curve must be generated. B-splines are generated to define the path. For best performance we minimize the number of knots in the splines and find their optimal locations. Using the spline fitting approach, a planar parabolic path is generated and used to further analyze the performance of our implementation.

Kinematic Synthesis of Spatial R-R Dyads for Path Following With Applications to Coupled Serial Chain Mechanisms

1999 ◽  
Vol 123 (3) ◽  
pp. 359-366 ◽  
Author(s):  
Venkat Krovi ◽  
G. K. Ananthasuresh ◽  
Vijay Kumar
Keyword(s):  
Linear System ◽  
Optimal Path ◽  
Closed Form Solution ◽  
Path Following ◽  
Form Solution ◽  
Dimensional Synthesis ◽  
Linear System Of Equations ◽  
Serial Chain ◽  
Position Problem ◽  
Additional Constraints

The dimensional synthesis of a spatial two revolute jointed dyad for path following tasks with applications to coupled serial chain mechanisms is presented. The precision point synthesis equations obtained using the rotation matrix approach form a rank-deficient linear system in the link-vector components. The nullspace of this rank-deficient linear system is derived analytically and interpreted geometrically. The nullspace vectors lead to the specification of additional constraints via the so-called auxiliary equations and to the solution of the linear system of equations. The geometry also allows the derivation of a closed form solution for the three design position problem. Finally, optimal path following by coupled R-R dyads is achieved by optimization over the free choice variables.

scholarly journals Best theory diagrams for multilayered plates considering multifield analysis

2017 ◽  
Vol 28 (16) ◽  
pp. 2184-2205 ◽  
Author(s):  
M Cinefra ◽  
E Carrera ◽  
A Lamberti ◽  
M Petrolo
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Governing Equations ◽  
Equilibrium Equations ◽  
Material Parameters ◽  
Stress Components ◽  
Minimum Number ◽  
Multilayered Plates ◽  
Carrera Unified Formulation ◽  
Definition Of

This work presents the best theory diagrams (BTDs) for multilayered plates involved in multifield problems (mechanical, thermal and electrical). A BTD is a curve that reports the minimum number of terms of a refined model for a given accuracy. The axiomatic/asymptotic technique is employed in order to detect the relevant terms, and the error is computed with respect to an exact or quasi-exact solution. The models that belong to the BTDs are constructed by means of a genetic algorithm and the Carrera Unified Formulation (CUF). The CUF defines the displacement field as an expansion of the thickness coordinate. The governing equations are obtained in terms of few fundamental nuclei, whose form does not depend on the particular expansion order that is employed. The Navier closed-form solution has been adopted to solve the equilibrium equations. The analyses herein reported are related to plates subjected to multifield loads: mechanical, thermal and electrical. The aim of this study is to evaluate the influence of the type of the load in the definition of the BTDs. In addition, the influence of geometry, material parameters and displacement/stress components are considered. The results suggest that the BTD and the CUF can be considered as tools to evaluate any structural theory against a reference solution. In addition, it has been found that the BTD definition is influenced to a great extent by the type of load.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

Capacity Analysis for Correlated Multi-Hop MIMO Channels under Colored Noise

2015 ◽  
Vol 1 ◽  
pp. 41
Author(s):  
Nguyen N. Tran ◽  
Ha X. Nguyen
Keyword(s):  
Computational Complexity ◽  
Mutual Information ◽  
Closed Form Solution ◽  
Optimal Solution ◽  
Form Solution ◽  
Maximization Problem ◽  
Capacity Analysis ◽  
Mimo Channels ◽  
Average Mutual Information ◽  
Channel Output

A capacity analysis for generally correlated wireless multi-hop multi-input multi-output (MIMO) channels is presented in this paper. The channel at each hop is spatially correlated, the source symbols are mutually correlated, and the additive Gaussian noises are colored. First, by invoking Karush-Kuhn-Tucker condition for the optimality of convex programming, we derive the optimal source symbol covariance for the maximum mutual information between the channel input and the channel output when having the full knowledge of channel at the transmitter. Secondly, we formulate the average mutual information maximization problem when having only the channel statistics at the transmitter. Since this problem is almost impossible to be solved analytically, the numerical interior-point-method is employed to obtain the optimal solution. Furthermore, to reduce the computational complexity, an asymptotic closed-form solution is derived by maximizing an upper bound of the objective function. Simulation results show that the average mutual information obtained by the asymptotic design is very closed to that obtained by the optimal design, while saving a huge computational complexity.

scholarly journals Geometric Average Asian Option Pricing with Paying Dividend Yield under Non-Extensive Statistical Mechanics for Time-Varying Model

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 828 ◽  
Author(s):  
Jixia Wang ◽  
Yameng Zhang
Keyword(s):  
Statistical Mechanics ◽  
Option Pricing ◽  
Asset Price ◽  
Closed Form Solution ◽  
Real Data ◽  
Form Solution ◽  
Asian Option ◽  
Time Varying ◽  
Dividend Yield ◽  
Geometric Average

This paper is dedicated to the study of the geometric average Asian call option pricing under non-extensive statistical mechanics for a time-varying coefficient diffusion model. We employed the non-extensive Tsallis entropy distribution, which can describe the leptokurtosis and fat-tail characteristics of returns, to model the motion of the underlying asset price. Considering that economic variables change over time, we allowed the drift and diffusion terms in our model to be time-varying functions. We used the I t o ^ formula, Feynman–Kac formula, and P a d e ´ ansatz to obtain a closed-form solution of geometric average Asian option pricing with a paying dividend yield for a time-varying model. Moreover, the simulation study shows that the results obtained by our method fit the simulation data better than that of Zhao et al. From the analysis of real data, we identify the best value for q which can fit the real stock data, and the result shows that investors underestimate the risk using the Black–Scholes model compared to our model.

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