Extracting Articulation Models from CAD Models of Parts With Curved Surfaces

2001 ◽  
Vol 124 (1) ◽  
pp. 106-114 ◽  
Author(s):  
Rajarishi Sinha ◽  
Satyandra K. Gupta ◽  
Christiaan J. J. Paredis ◽  
Pradeep K. Khosla
Keyword(s):  
Contact Mechanics ◽  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Curved Surfaces ◽  
Global Motion ◽  
Intended Behavior ◽  
Cad Models ◽  
Constraint Method ◽  
Motion Behavior ◽  
Algebraic Constraint

In an assembly, degrees of freedom are realized by creating mating features that permit relative motion between parts. In complex assemblies, interactions between individual degrees of freedom may result in a behavior different from the intended behavior. In addition, current methods perform assembly reasoning by approximating curved surfaces as piecewise linear surfaces. Therefore, it is important to be able to reason about assemblies using exact representations of curved surfaces; verify global motion behavior of parts in the assembly; and create motion simulations of the assembly by examination of the geometry and material properties. In this paper, we present a linear algebraic constraint method to automatically construct the space of allowed instantaneous motions of an assembly from the geometry of its constituent parts. Our work builds on previous work on linear contact mechanics and curved surface contact mechanics. We enumerate the conditions under which general curved surfaces can be represented using a finite number of constraints that are linear in the instantaneous velocities. We compose such constraints to build a space of allowed instantaneous velocities for the assembly. The space is then described as a set-theoretic sum of contact-preserving and contact-breaking subspaces. Analysis of each subspace provides feedback to the designer, which we demonstrate through the use of an example assembly—a 4-part mechanism. Finally, the results of the analysis of a 4-bar linkage are compared to those from mechanism theory.

Nonlinear Dynamics of One-Way Clutches in Belt-Pulley Systems

2003 ◽  
Author(s):  
Farong Zhu ◽  
Robert G. Parker
Keyword(s):  
Nonlinear Dynamics ◽  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Primary Resonance ◽  
Harmonic Balance Method ◽  
Excitation Amplitude ◽  
Relative Displacement ◽  
Second Primary ◽  
Arc Length ◽  
The One

One-way clutches are frequently used in the serpentine belt accessory drives of automobiles and heavy vehicles. The clutch plays a role similar to a vibration absorber in order to reduce belt/pulley vibration and noise and increase belt life. This paper analyzes a two-pulley system where the driven pulley has a one-way clutch between the pulley and accessory shaft that engages only for positive relative displacement between these components. The belt is modeled with linear springs that transmit torque from the driving pulley to the accessory pulley. The one-way clutch is modeled as a piecewise linear spring with discontinuous stiffness that separates the driven pulley into two degrees of freedom (DOF). The harmonic balance method (HBM) combined with arc-length continuation is employed to illustrate the nonlinear dynamic behavior of the one-way clutch. HBM with arc-length continuation yields the stable and unstable periodic solutions for given parameters. These solutions are examined across a range of excitation frequencies. The results are confirmed by numerical integration and the widely used bifurcation software AUTO. At the first primary resonance, most of the responses are aperiodic, including quasiperiodic and chaotic solutions. At the second primary resonance, the peak bends to the left with classical softening nonlinearity because clutch disengagement decouples the pulley and the accessory over portions of the response period. The dependence on system parameters such as clutch stiffness, excitation amplitude, and inertia ratio between the pulley and accessory is studied to characterize the nonlinear dynamics across a range of conditions.

Synthesis of Planar, Shape-Changing Rigid-Body Mechanisms

2006 ◽  
Author(s):  
Brian M. Korte ◽  
Andrew P. Murray ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Shape Change ◽  
Piecewise Linear ◽  
Single Chain ◽  
Open Chain ◽  
Revolute Joints ◽  
Planar Shape ◽  
Rigid Body Displacement ◽  
Planar Linkages

This paper presents a procedure to synthesize planar linkages, composed of rigid links and revolute joints, capable of approximating a shape change defined by a set of curves. These “morphing curves” differ from each other by a combination of rigid-body displacement and shape change. Rigid link geometry is determined through analysis of piecewise linear curves to achieve shape-change approximation, and increasing the number of links improves the approximation. A mechanism is determined through connecting the rigid links into a single chain and adding dyads to eliminate degrees of freedom. The procedure is applied to two open-chain examples.

scholarly journals THREE SIMPLE HEURISTICS MATHEMATICAL PROOFS ON LASSO THEORY

2020 ◽  
Vol 38 (2) ◽  
pp. 243
Author(s):  
Carlos José dos REIS ◽  
Laerte Dias de CARVALHO ◽  
Lucas Monteiro CHAVES ◽  
Devanil Jaques de SOUZA
Keyword(s):  
Unbiased Estimator ◽  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Tuning Parameter ◽  
Geometrical Approach ◽  
Mathematical Proofs ◽  
Selection Operator ◽  
Simple Heuristics

Three relevant facts about the least absolute shrinkage and selection operator (Lasso) are studied: The estimatives follows piecewise linear curves in relation to tuning parameter, the number of nonzero selected covariates is an unbiased estimator of its degrees of freedom and when the number of covariates p is greater than the numbers of observations n at most n covariates are selected. These results are well known and described in the literature, but with no simple demonstrations. We present, based on a geometrical approach, simple and intuitive heuristics proofs for these results.

scholarly journals Towards an improved description of ocean uncertainties: effect of local anamorphic transformations on spatial correlations

2011 ◽  
Vol 8 (5) ◽  
pp. 2147-2195 ◽  
Author(s):  
J.-M. Brankart ◽  
C.-E. Testut ◽  
D. Béal ◽  
M. Doron ◽  
C. Fontana ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Correlation Radius ◽  
Correlation Structure ◽  
General Tendency ◽  
Spatial Correlations ◽  
Parameter Uncertainties ◽  
Large Size ◽  
Observation Network ◽  
Spatial Correlation Structure

Abstract. The objective of this paper is to investigate if the description of ocean uncertainties can be significantly improved by applying a local anamorphic transformation to each model variable, and by making the assumption of joint Gaussianity for the transformed variables, rather than for the original variables. For that purpose, it is first argued that a significant improvement can already be obtained by deriving the local transformations from a simple histogram description of the marginal distributions. Two distinctive advantages of this solution for large size applications are the conciseness and the numerical efficiency of the description. Second, various oceanographic examples are used to evaluate the effect of the resulting piecewise linear local anamorphic transformations on the spatial correlation structure. These examples include (i) stochastic ensemble descriptions of the effect of atmospheric uncertainties on the ocean mixed layer, and of wind uncertainties or parameter uncertainties on the ecosystem, and (ii) non-stochastic ensemble descriptions of forecast uncertainties in current sea ice and ecosystem pre-operational developments. The results indicate that (i) the transformation is accurate enough to faithfully preserve the correlation structure if the joint distribution is already close to Gaussian, and (ii) the transformation has the general tendency of increasing the correlation radius as soon as the spatial dependence between random variables becomes nonlinear, with the important consequence of reducing the number of degrees of freedom in the uncertainties, and thus increasing the benefit that can be expected from a given observation network.

A Method for Solving Large-Scale Multiloop Constrained Dynamical Systems Using Structural Decomposition

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Tao Xiong ◽  
Jianwan Ding ◽  
Yizhong Wu ◽  
Liping Chen ◽  
Wenjie Hou
Keyword(s):  
Dynamical Systems ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
The State ◽  
State Variables ◽  
Structural Decomposition ◽  
Multiple Degrees Of Freedom ◽  
Constraint Equations ◽  
Constrained Dynamical Systems ◽  
Algebraic Constraint

A structural decomposition method based on symbol operation for solving differential algebraic equations (DAEs) is developed. Constrained dynamical systems are represented in terms of DAEs. State-space methods are universal for solving DAEs in general forms, but for complex systems with multiple degrees-of-freedom, these methods will become difficult and time consuming because they involve detecting Jacobian singularities and reselecting the state variables. Therefore, we adopted a strategy of dividing and conquering. A large-scale system with multiple degrees-of-freedom can be divided into several subsystems based on the topology. Next, the problem of selecting all of the state variables from the whole system can be transformed into selecting one or several from each subsystem successively. At the same time, Jacobian singularities can also be easily detected in each subsystem. To decompose the original dynamical system completely, as the algebraic constraint equations are underdetermined, we proposed a principle of minimum variable reference degree to achieve the bipartite matching. Subsequently, the subsystems are determined by aggregating the strongly connected components in the algebraic constraint equations. After that determination, the free variables remain; therefore, a merging algorithm is proposed to allocate these variables into each subsystem optimally. Several examples are given to show that the proposed method is not only easy to implement but also efficient.

Lateral Bifurcation Behavior of a Four-Axle Railway Passenger Car

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
Xuejun Gao ◽  
Yinghui Li ◽  
Qing Gao
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Lateral Motion ◽  
Dynamical Equations ◽  
Chaotic Motions ◽  
Passenger Car ◽  
Railway Passenger ◽  
Bifurcation Behavior

We investigate the kinematics and dynamics of a high-speed four-axle railway passenger car, which has 17 degrees of freedom, considering the lateral motion, roll and yaw angles of the car body and the bogie frame, and the lateral motion and yaw angle of the four wheelsets. The creep forces and the flange forces between the oscillating wheels and the rails are main nonlinearities and can be estimated by the Vermeulen–Johnson creep force laws and a piecewise linear function, respectively. The dynamical equations for the motion of the vehicle running with constant speed along an ideal, rigid, straight, and perfect track are formulated, and the lateral bifurcation behavior of the vehicle system is investigated numerically. The results indicate that both stable and unstable orbits are obtained, and the linear and nonlinear critical speeds are determined as well. Several kinds of dynamical behaviors, such as stationary equilibrium point, symmetric or asymmetric periodic oscillations, and symmetric or asymmetric chaotic motions, are found and described in great detail within the investigated speed range.

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