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.

Preliminaries for a Spherical Compliant Mechanism: Pseudo-Rigid-Body Model Kinematics

2007 ◽  
Author(s):  
Saurabh Jagirdar ◽  
Craig P. Lusk
Keyword(s):  
Rigid Body ◽  
Compliant Mechanism ◽  
Beam Angle ◽  
Body Model ◽  
Spherical Mechanisms ◽  
Characteristic Radius ◽  
Rigid Body Model ◽  
Limiting Case

The kinematic portion of a pseudo-rigid-body model (PRBM) is developed as a generalization from planar to spherical mechanisms. The topology of the spherical compliant segment and its rigid-body equivalent are derived from planar models by analogy. The nomenclature for the spherical PRBM is chosen to facilitate comparison with the planar PRBM. The motion of the compliant segment is calculated using FEA and PRBM parameters are determined. The characteristic radius and parametric angle coefficient are found to decrease as the angle subtended by the beam increases. The parameterization limit increases with increasing beam angle. The spherical PRBM is identical to the planar PRBM in the limiting case when beam angles become very small.

Parametric Deflection Approximations for Initially Curved, Large-Deflection Beams in Compliant Mechanisms

1996 ◽  
Author(s):  
Larry L. Howell ◽  
Ashok Midha
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Curved Beam ◽  
Analysis And Design ◽  
Body Model ◽  
Rigid Body Model ◽  
Fundamental Type ◽  
Applied Forces ◽  
Flexible Member

Abstract The analysis of systems containing highly flexible members is made difficult by the nonlineararities caused by large deflections of the flexible members. The analysis and design of many such systems may be simplified by using pseudo-rigid-body approximations in modeling the flexible members. The pseudo-rigid-body model represents flexible members as rigid links, joined at pin joints with torsional springs. Appropriate values for link lengths and torsional spring stiffnesses are determined such that the deflection path and force-deflection relationships are modeled accurately. Pseudo-rigid-body approximations have been developed for initially straight beams with externally applied forces at the beam end. This work develops approximations for another fundamental type of flexible member, the initially curved beam with applied force at the beam end. This type of flexible member is commonly used in compliant mechanisms. An example of the use of the resulting pseudo-rigid-body approximations in compliant mechanisms is included.

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.

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 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.

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.

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.

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).

Pseudo-Rigid-Body Model for the Flexural Beam With an Inflection Point in Compliant Mechanisms

2017 ◽  
Vol 9 (3) ◽  
Author(s):  
Shun-Kun Zhu ◽  
Yue-Qing Yu
Keyword(s):  
Rigid Body ◽  
Inflection Point ◽  
Compliant Mechanisms ◽  
Angular Displacement ◽  
Flexible Beam ◽  
Body Model ◽  
Numerical Result ◽  
Characteristic Radius ◽  
Rigid Body Model ◽  
Flexural Beam

The pseudo-rigid-body model (PRBM) used to simulate compliant beams without inflection point had been well developed. In this paper, two types of PRBMs are proposed to simulate the large deflection of flexible beam with an inflection point in different configurations. These models are composed of five rigid links connected by three joints added with torsional springs and one hinge without spring representing the inflection point in the flexural beam. The characteristic radius factors of the PRBMs are determined by solving the objective function established according to the relative angular displacement of the two rigid links jointed by the hinge via genetic algorithm. The spring stiffness coefficients are obtained using a linear regression technique. The effective ranges of these two models are determined by the load index. The numerical result shows that both the tip locus and inflection point of the flexural beam with single inflection can be precisely simulated using the model proposed in this paper.

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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