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.

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).

scholarly journals Design and Validation of a Single-SOI-Wafer 4-DOF Crawling Microgripper

Micromachines ◽  
2019 ◽  
Vol 10 (6) ◽  
pp. 376 ◽  
Author(s):  
Matteo Verotti ◽  
Alvise Bagolini ◽  
Pierluigi Bellutti ◽  
Nicola Pio Belfiore
Keyword(s):  
Finite Element Analysis ◽  
Rigid Body ◽  
Compliant Mechanism ◽  
Silicon On Insulator ◽  
Element Analysis ◽  
Deep Reactive Ion Etching ◽  
Theoretical Simulation ◽  
Body Model ◽  
Replacement Method ◽  
Rigid Body Model

This paper deals with the manipulation of micro-objects operated by a new concept multi-hinge multi-DoF (degree of freedom) microsystem. The system is composed of a planar 3-DoF microstage and of a set of one-DoF microgrippers, and it is arranged is such a way as to allow any microgripper to crawl over the stage. As a result, the optimal configuration to grasp the micro-object can be reached. Classical algorithms of kinematic analysis have been used to study the rigid-body model of the mobile platform. Then, the rigid-body replacement method has been implemented to design the corresponding compliant mechanism, whose geometry can be transferred onto the etch mask. Deep-reactive ion etching (DRIE) is suggested to fabricate the whole system. The main contributions of this investigation consist of (i) the achievement of a relative motion between the supporting platform and the microgrippers, and of (ii) the design of a process flow for the simultaneous fabrication of the stage and the microgrippers, starting from a single silicon-on-insulator (SOI) wafer. Functionality is validated via theoretical simulation and finite element analysis, whereas fabrication feasibility is granted by preliminary tests performed on some parts of the microsystem.

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.

The Development of Force-Deflection Relationships for Compliant Mechanisms

1994 ◽  
Author(s):  
Larry L. Howell ◽  
Ashok Midha
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Virtual Work ◽  
Compliant Mechanism ◽  
Flexible Link ◽  
Model Concept ◽  
Body Model ◽  
Design Flexibility ◽  
Rigid Body Model ◽  
Manufacturing Time

Abstract The advantages of compliant or flexible link mechanisms include increased design flexibility and reduction in manufacturing time and cost. The analysis of such mechanisms may be difficult and time consuming due to the nonlinearities introduced by large deflections. Also, unlike rigid-body mechanisms, the type and form of motion of a compliant mechanism is dependent on the location and magnitude of applied loads. The pseudo-rigid-body model concept has been developed to simplify the analysis of compliant mechanisms by allowing them to be modeled as rigid-link mechanisms with springs. This work uses the principle of virtual work and the pseudo-rigid-body model concept to develop force-deflection relationships for compliant mechanisms. Several examples are presented, and general design equations are derived for pseudo-rigid-body four-bar and slider-crank mechanisms.

A Family of Butterfly Flexural Joints: Q-LITF Pivots

2011 ◽  
Author(s):  
Xu Pei ◽  
Jingjun Yu ◽  
Shusheng Bi ◽  
Guanghua Zong
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Rigid Body ◽  
Rigid Bodies ◽  
The Other ◽  
Element Analysis ◽  
Leaf Type ◽  
Center Shift ◽  
Body Model ◽  
Rigid Body Model

The Leaf-type Isosceles-Trapezoidal Flexural (LITF) pivot consists of two compliant beams and two rigid-bodies. For a single LITF pivot, the range of motion is small while the center-shift is relatively large. The capability of performance can be improved greatly by the combination of four LITF pivots. Base on the pseudo-rigid-body model (PRBM) of a LITF pivot, a method to construct the Quadri-LITF pivots is presented by regarding a single LITF pivot (or double-LITF pivot) as a the configurable flexure module. Ten types of Q-LITF pivots are synthesized. Compared with the single LIFT pivot, the stroke becomes larger, and stiffness becomes smaller. Four of them have the increased center-shift. The other four have the decreased center-shift. One of the quadruple LITF pivots is selected as the examples to explain the proposed method. The comparison between PRBM and Finite Element Analysis (FEA) result shows the validity and effectiveness of the method.

Spatial-Beam Large-Deflection Equations and Pseudo-Rigid-Body Model for Axisymmetric Cantilever Beams

2011 ◽  
Author(s):  
Issa A. Ramirez ◽  
Craig P. Lusk
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Rigid Body ◽  
Three Dimensional ◽  
Vertical Axis ◽  
Analysis Model ◽  
Element Analysis ◽  
Body Model ◽  
Straight Beam ◽  
Rigid Body Model

The kinematic equations for approximating the deflection of a three-dimensional cantilever beam were developed. The numerical equations were validated with a Finite Element Analysis program. With these equations, a pseudo-rigid-body model (PRBM) for an axisymmetric straight beam was developed. The axisymmetric PRBM consists of a spherical joint connecting two rigid links. The location of the deformed end of the beam is determined by two angles and the characteristic radius factor. The angle of the beam with respect to the vertical axis depends on the direction of the force with respect to the undeformed coordinate system. The Pearson’s correlation coefficient for the Finite Element Analysis model and the numerical integration is 0.952.

A Numerical Method for Position Analysis of Compliant Mechanisms With More Degrees of Freedom Than Inputs

2010 ◽  
Author(s):  
Quentin T. Aten ◽  
Shannon A. Zirbel ◽  
Brian D. Jensen ◽  
Larry L. Howell
Keyword(s):  
Potential Energy ◽  
Rigid Body ◽  
Equilibrium Position ◽  
Degrees Of Freedom ◽  
Compliant Mechanisms ◽  
Virtual Work ◽  
Compliant Mechanism ◽  
Loop Equation ◽  
Body Model ◽  
Rigid Body Model

An under-actuated or underconstrained compliant mechanism may have a determined equilibrium position because its energy storage elements cause a position of local minimum potential energy. The minimization of potential energy (MinPE) method is a numerical approach to finding the equilibrium position of compliant mechanisms with more degrees of freedom (DOF) than inputs. Given the pseudo-rigid-body model of a compliant mechanism, the MinPE method finds the equilibrium position by solving a constrained optimization problem: minimize the potential energy stored in the mechanism, subject to the mechanism’s vector loop equation(s) being equal to zero. The MinPE method agrees with the method of virtual work for position and force determination for under-actuated 1-DOF and 2-DOF pseudo-rigid-body models. Experimental force-deflection data is presented for a fully compliant constant-force mechanism. Because the mechanism’s behavior is not adequately modeled using a 1-DOF pseudo-rigid-body model, a 13-DOF pseudo-rigid-body model is developed and solved using the MinPE method. The MinPE solution is shown to agree well with non-linear finite element analysis and experimental force-displacement data.

A Pseudo-Rigid-Body Model for Spherical Mechanisms: The Kinematics and Stiffness of a Compliant Curved Beam

2008 ◽  
Author(s):  
Alejandro Leo´n ◽  
Saurabh Jagirdar ◽  
Craig P. Lusk
Keyword(s):  
Rigid Body ◽  
Curved Beam ◽  
Beam Angle ◽  
Element Analysis ◽  
Body Model ◽  
Spherical Mechanisms ◽  
Characteristic Radius ◽  
Rigid Body Model ◽  
Spherical Mechanism ◽  
Spherical Motion

A pseudo-rigid-body model (PRBM) which describes a class of curved compliant beams in terms of spherical mechanism kinematics was developed. The topology of the spherical compliant segment and its rigid-body equivalent were chosen to be analogous to planar models. The nomenclature for the spherical PRBM was also chosen to facilitate comparison with planar models. The motion of the compliant segment was calculated Finite Element Analysis and the PRBM parameters were determined. The characteristic radius and parametric angle coefficient were found to decrease as the angle subtended by the beam increases. The kinematic and elastic parameterization limits of the model increase with increasing beam angle. The stiffness of the beam is described by two separate spring elements, which describe the appropriate combination of moment and force which produces spherical motion. A previous planar PRBM is shown to be the small angle limit of the new spherical PRBM.

A Novel Fully Compliant Planar Linear-Motion Mechanism

2004 ◽  
Author(s):  
Neal B. Hubbard ◽  
Jonathan W. Wittwer ◽  
John A. Kennedy ◽  
Daniel L. Wilcox ◽  
Larry L. Howell
Keyword(s):  
Linear Motion ◽  
Element Analysis ◽  
Single Plane ◽  
Motion Mechanism ◽  
Body Model ◽  
Straight Line ◽  
Structural Error ◽  
Rigid Body Model ◽  
In Series ◽  
Force Displacement

A new fully compliant linear-motion mechanism, called the XBob, is presented. The mechanism is based on the pseudo-rigid-body model (PRBM) of a system of Roberts approximate straight-line mechanisms combined in series and parallel. It can be fabricated in a single plane and has a linear force-displacement relationship. Symmetry and compliance compensate for the structural error inherent in the Roberts mechanism, resulting in precise straight-line motion. The device is designed and its motion and force-displacement relations are predicted by the PRBM. The design is validated using finite element analysis and experimental results.

Modeling and Optimization of a Miniature Elastomeric Compliant Mechanism Using a 3-Spring Pseudo Rigid Body Model

2013 ◽  
Author(s):  
Dana Vogtmann ◽  
Satyandra K. Gupta ◽  
Sarah Bergbreiter
Keyword(s):  
Finite Element Analysis ◽  
Rigid Body ◽  
Compliant Mechanism ◽  
Maximum Error ◽  
Correction Factors ◽  
Element Analysis ◽  
Body Model ◽  
Fea Model ◽  
Rigid Body Model ◽  
Robotic Leg

This paper extends a previously developed Pseudo Rigid Body (PRB) analytical model for miniature elastomeric joints by introducing correction factors for joints with geometry not previously considered. Inclusion of these correction factors has resulted in an increase in the accuracy of the model from 20% to within 3% in bending and from 25% to within 7% in tension, when compared to equivalent Finite Element Analysis (FEA) models. Additionally, using the PRB model, a robotic leg with four elastomeric joints has been modeled, resulting in a maximum error of 12% when compared to an equivalent FEA model. Finally, the PRB model was used to optimize the robotic leg for minimum motor torque required to drive a hexapedal robot with six identical legs.

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