scholarly journals A 3-D Pseudo-Rigid Body Model for Rectangular Cantilever Beams With an Arbitrary Force End-Load

2014 ◽  
Author(s):  
Jairo Chimento ◽  
Craig Lusk ◽  
Ahmad Alqasimi
Keyword(s):  
Rigid Body ◽  
Cross Sections ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Neutral Axis ◽  
Spatial Behavior ◽  
Model Parameters ◽  
Cantilever Beams ◽  
Body Model ◽  
Rigid Body Model

This paper presents the first three-dimensional pseudo-rigid body model (3-D PRBM) for straight cantilever beams with rectangular cross sections and spatial motion. Numerical integration of a system of differential equations yields approximate displacement and orientation of the beam’s neutral axis at the free-end, and curvatures of the neutral axis at the fixed-end. This data was used to develop the 3-D PRBM which consists of two torsional springs connecting two rigid links for a total of 2 degrees of freedom (DOF). The 3-D PRBM parameters that are comparable with existing 2-D model parameters are characteristic radius factor (means: γ = 0.8322), bending stiffness coefficient (means: KΘ = 2.5167) and parametric angle coefficient (means: cΘ = 1.2501). New parameters are introduced in the model in order to capture the spatial behavior of the deflected beam including two parametric angle coefficients (means: cΨ = 1.0714; cΦ = 1.0087).

A Pseudo-Rigid-Body Model for Rolling-Contact Compliant Beams

2007 ◽  
Author(s):  
Allen B. Mackay ◽  
Spencer P. Magleby ◽  
Larry L. Howell
Keyword(s):  
Rigid Body ◽  
Rolling Contact ◽  
Model Parameters ◽  
Displacement Curve ◽  
Cantilever Beams ◽  
Body Model ◽  
Rigid Body Model ◽  
Contact Surfaces ◽  
Definition Of ◽  
Force Displacement

This paper presents a pseudo-rigid-body model (PRBM) for rolling-contact compliant beams (RCCBs). The loading conditions and boundary conditions for the RCCB can be simplified to an equivalent cantilever beam that has the same force-deflection characteristics as the RCCB. Building on the PRBM for cantilever beams, this paper defines a model for the force-deflection relationship for RCCBs. The definition of the RCCB PRBM includes the pseudo-rigid-body model parameters that determine the shape of the beam, the length of the corresponding pseudo-rigid-body links and the stiffness of the equivalent torsional spring. The behavior of the RCCB is parameterized in terms of a single parameter defined as clearance, or the distance between the contact surfaces. RCCBs exhibit a unique force-displacement curve where the force is inversely proportional to the clearance squared.

A 3D Pseudo-Rigid-Body Model for Large Spatial Deflections of Rectangular Cantilever Beams

2006 ◽  
Author(s):  
Nathan O. Rasmussen ◽  
Jonathan W. Wittwer ◽  
Robert H. Todd ◽  
Larry L. Howell ◽  
Spencer P. Magleby
Keyword(s):  
Rigid Body ◽  
Cross Sections ◽  
Compliant Mechanisms ◽  
Circular Path ◽  
Cantilever Beams ◽  
Spherical Joint ◽  
3 Dimensional ◽  
Body Model ◽  
Rigid Body Model ◽  
Out Of Plane

The design of compliant mechanisms has been aided by the development of pseudo-rigid-body models to predict the motion of flexible members undergoing large displacements. Many of these models are based on the fact that the end of a cantilever beam follows a near-circular path when planar loads are applied. This paper shows that the application of 3-dimensional end-loading causes a beam to follow a near-spherical path, even for beams with non-circular cross-sections. A 3D pseudo-rigid-body model is presented that allows the motion of an end-loaded rectangular beam to be predicted using a rigid link and a spherical joint. Two sets of deflection limits for 0.5% error are presented and shown to be dependent upon the aspect ratio of the cross-section of the beam. The model has the potential for aiding in the design of spatial compliant mechanisms and analysis of planar compliant mechanisms undergoing large out-of-plane motions.

Classification of Compliant Mechanisms and Determination of the Degrees of Freedom Using the Concepts of Compliance Number and Pseudo-Rigid-Body Model

2019 ◽  
Author(s):  
Pratheek Bagivalu Prasanna ◽  
Ashok Midha ◽  
Sushrut G. Bapat
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Body Model ◽  
Active Compliance ◽  
Kinematic Behavior ◽  
Rigid Body Model

Abstract Understanding the kinematic properties of a compliant mechanism has always proved to be a challenge. A concept of compliance number offered earlier emphasized the development of terminology that aided in its determination. A method to evaluate the elastic degrees of freedom associated with the flexible segments/links of a compliant mechanism using the pseudo-rigid-body model (PRBM) concept is provided. In this process, two distinct classes of compliant mechanisms are developed involving: (i) Active Compliance and (ii) Passive Compliance. Furthermore, these also aid in a better characterization of the kinematic behavior of a compliant mechanism. A more lucid interpretation of the significance of compliance number is provided. Applications of this method to both active and passive compliant mechanisms are exemplified. Finally, an experimental procedure that aids in visualizing the degrees of freedom as calculated is presented.

scholarly journals Flexible Model for Miro-launcher Dynamics

2019 ◽  
Vol 304 ◽  
pp. 07013
Author(s):  
Teodor-Viorel Chelaru ◽  
Valentin Pana ◽  
Alexandru Iulian Onel ◽  
Tudorel-Petronel Afilipoae ◽  
Andrei Filip Cojocaru ◽  
...  
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Elastic Model ◽  
Six Degrees Of Freedom ◽  
Body Model ◽  
Rigid Body Model ◽  
Three Stages ◽  
Flight Parameters ◽  
Elastic Modes ◽  
Flexible Model

The paper presents aspects regarding flexible model used for describing the dynamics of the three stages micro-launcher. This work analyses transverse flexible oscillations. By the hypotheses adopted, the flexibility problem will be reduced to a group of equations that will be attached to the rigid body model with six degrees of freedom, thus obtaining an elastic model for the launcher. The results analysed will be the flight parameters the launcher, with the influence of the elastic modes considered. The novelty of the paper consists in highlighting the influence of elasticity on the launcher control problem.

The Analysis of a Simplified 2R Pseudo-Rigid-Body Model with Moment Load

2012 ◽  
Vol 224 ◽  
pp. 18-23
Author(s):  
Yun Jiao Zhang ◽  
Guo Wu Wei ◽  
Jian Sheng Dai
Keyword(s):  
Rigid Body ◽  
Objective Function ◽  
Compliant Mechanisms ◽  
Three Dimensional ◽  
Body Model ◽  
Design Variables ◽  
Characteristic Radius ◽  
Rigid Body Model ◽  
Analysis And Synthesis ◽  
Moment Load

Pseudo-rigid-body model (PRBM) method, which simplifies the geometrical nonlinear analysis, has become an important tool for the analysis and synthesis of compliant mechanisms. In this paper, a simplified 2R PRBM with two rigid links and two torsion springs is proposed. The characteristic radius factor and stiffness coefficients are selected as the design variables; in order to be better to simulate the tip point and tip slope, a three-dimensional objective function is formulated to optimize the new pseudo-rigid-body model. It is revealed in this paper that the precision of the tip point simulation can be improved when the coefficient of the tip slope error in the objective function is reduced.

A Methodology for Determining Static Mode Shapes of a Compliant Mechanism Using the Pseudo-Rigid-Body Model (PRBM) Concept and the Degrees-of-Freedom Analysis

2019 ◽  
Author(s):  
Sushrut G. Bapat ◽  
Pratheek Bagivalu Prasanna ◽  
Ashok Midha
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Mode Shapes ◽  
Model Concept ◽  
Static Mode ◽  
Displacement Boundary ◽  
Body Model ◽  
Rigid Body Model

Abstract Traditionally, the deflected configuration of compliant segments is determined through rigorous mathematical analysis using Newtonian mechanics. Application of these principles in evaluating the deformed configuration of compliant mechanisms, containing a variety of segment types, becomes cumbersome. This paper introduces a methodology to determine the expected deflected configuration(s) of a compliant mechanism, for a given set of load and/or displacement boundary conditions. The method utilizes the principle of minimum total potential energy, in conjunction with the degrees-of-freedom analysis and the pseudo-rigid-body model concept. The static mode shape(s) of compliant segments are integrated in identifying the possible functional configuration(s) of a given compliant mechanism’s structural configuration. The methodology, in turn, also facilitates the in situ determination of the deformed configuration of the constituent compliant segments. It thus assists in the identification of an appropriate pseudo-rigid-body model for design and analysis of a compliant mechanism.

Joint reactions in rigid or flexible body mechanisms with redundant constraints

2012 ◽  
Vol 60 (3) ◽  
pp. 617-626 ◽  
Author(s):  
M. Wojtyra ◽  
J. Frączek
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Flexible Body ◽  
Flexible Bodies ◽  
Redundant Constraints ◽  
Constraint Equations ◽  
Body Model ◽  
Rigid Body Model ◽  
Flexible Models

Abstract The problem of joint reactions indeterminacy, in engineering simulations of rigid body mechanisms is most often caused by redundant constraints which are defined as constraints that can be removed without changing the kinematics of the system. In order to find a unique set of all joint reactions in an overconstrained system, it is necessary to reject the assumption that all bodies are rigid. Flexible bodies introduce additional degrees of freedom to the mechanism, which usually makes the constraint equations independent. Quite often only selected bodies are modelled as the flexible ones, whereas the other remain rigid. In this contribution it is shown that taking into account flexibility of selected mechanism bodies does not guarantee that unique joint reactions can be found. Problems typical for redundant constraints existence are encountered in partially flexible models, which are not overconstrained. A case study of a redundantly constrained spatial mechanism is presented. Different approaches to the mechanism modelling, ranging from a purely rigid body model to a fully flexible one, are investigated and the obtained results are compared and discussed.

Improved Pseudo-Rigid-Body Model Parameter Values for End-Force-Loaded Compliant Beams

2004 ◽  
Author(s):  
Joby Pauly ◽  
Ashok Midha
Keyword(s):  
Rigid Body ◽  
Design Process ◽  
Compliant Mechanism ◽  
Model Parameters ◽  
Body Model ◽  
Axial Tensile ◽  
Rigid Body Model ◽  
Analysis And Synthesis ◽  
Parameter Values ◽  
Compliant Mechanism Design

Pseudo-rigid-body models help expedite the compliant mechanism design process by aiding the analysis and synthesis of candidate design solutions, using loop-closure techniques for rigid-body mechanisms. Opportunities for improvement were observed in the values of pseudo-rigid-body model parameters for compliant beams with nearly axial, tensile end force loads. This paper presents improved values for the affected parameters.

Pseudo-Rigid-Body Models for End-Loaded Heavy Cantilever Beams

2015 ◽  
Author(s):  
Philip J. Logan ◽  
Craig P. Lusk
Keyword(s):  
Rigid Body ◽  
Compliant Mechanism ◽  
Elastic Beam ◽  
Model Parameters ◽  
Cantilever Beams ◽  
Distributed Load ◽  
Rigid Body Model ◽  
Mathematical Techniques ◽  
Calculated Model

The large deflection of cantilever beams has been widely studied. A number of models and mathematical techniques have been utilized in predicting the path coordinates and load-deflection relationships of such beams. The Pseudo-Rigid-Body Model (PRBM) is one such method which replaces the elastic beam with rigid links of a parameterized pivot location and torsional spring stiffness. In this paper, the PRBM method is extended to include cases of a constant distributed load combined with a parallel endpoint force. The phase space of the governing differential equations is used to store information relevant to the characterization of the PRBM parameters. Correction factors are also given to decrease the error in the load-deflection relationship and extend the angular range of the model, thereby further aiding compliant mechanism design. Our calculations suggest a simple way of representing the effective torque caused by a distributed load in a PRBM as a function of easily calculated model parameters.

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