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.

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).

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.

Force-Displacement Model of the FlexSuRe™ Spinal Implant

2010 ◽  
Author(s):  
Eric Stratton ◽  
Larry Howell ◽  
Anton Bowden
Keyword(s):  
Rigid Body ◽  
Virtual Work ◽  
Implant Design ◽  
Element Analysis ◽  
Spinal Implant ◽  
Body Model ◽  
Flexion Extension ◽  
Rigid Body Model ◽  
Displacement Model ◽  
Force Displacement

This paper presents modeling of a novel compliant spinal implant designed to reduce back pain and restore function to degenerate spinal disc tissues as well as provide a mechanical environment conducive to healing of the tissues. Modeling was done through the use of the pseudo-rigid-body model. The pseudo-rigid-body model is a 3 DOF mechanism for flexion-extension (forward-backward bending) and a 5 DOF mechanism for lateral bending (side-to-side). These models were analyzed using the principle of virtual work to obtain the force-deflection response of the device. The model showed good correlation to finite element analysis and experimental results. The implant may be particularly useful in the early phases of implant design and when designing for particular biological 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.

Design of a New Fully Compliant Translational Joint via Straight-Line Motion Mechanism Based Method

2019 ◽  
Author(s):  
Sonia C. García ◽  
Juan A. Gallego-Sanchez
Keyword(s):  
Rigid Body ◽  
Symmetry Axis ◽  
Initial Position ◽  
Element Analysis ◽  
Motion Mechanism ◽  
Body Model ◽  
Straight Line ◽  
Rigid Body Model ◽  
Translational Joint ◽  
Force Displacement

Abstract A Compliant Translational Joint (CTJ) is designed via Straight-Line Motion Mechanism Method. The designed CTJ is based on the Pseudo-Rigid-Body-Model (PRBM) of a modified Scott-Russell Mechanism. The precision of the straight-line motion of the rigid-body mechanism adjusts to a straight-line to a 99.6% while the compliant version adjusts to a 99.9%. The novelty of the design is given by the way the CTJ is designed, the performance of the CTJ is achieved by mirroring the mechanism about an axis tangent to the path of the mechanism and that passes through the initial position of the coupler point at the symmetry axis of the path. The CTJ motion is predicted by the PRBM. The force-displacement relations and the frequency modes of the CTJ are analyzed using finite element analysis (FEA).

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.

Design and Testing of a Compliant Floating-Opposing-Arm (FOA) Centrifugal Clutch

2000 ◽  
Author(s):  
Nathan B. Crane ◽  
Larry L. Howell ◽  
Brent L. Weight
Keyword(s):  
Rigid Body ◽  
Test Data ◽  
Body Model ◽  
Model Predictions ◽  
Rigid Body Model ◽  
Contact Surfaces ◽  
Design And Testing

Abstract A floating-opposing-arm (FOA) centrifugal clutch is presented that uses compliant segments to reduce the part count and increase manufacturability. The clutch performs all of the functions of a centrifugal clutch, but consists of only two pieces. Torque is increased by connecting aggressive and non-aggressive contact surfaces in connected pairs. This arrangement increases the torque output of the FOA clutch by over 100% relative to a commercial one-piece compliant centrifugal clutch design of the same size and material. Yet, since this design is compliant, it remains simple to manufacture. This clutch is presented and modeled using the pseudo-rigid-body-model (PRBM) technique. The model predictions are compared to test data from five prototypes. The FOA clutch is also demonstrated in a gasoline-powered string trimmer.

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