A Three-Spring Pseudorigid-Body Model for Soft Joints With Significant Elongation Effects

2016 ◽  
Vol 8 (6) ◽  
Author(s):  
Venkatasubramanian Kalpathy Venkiteswaran ◽  
Hai-Jun Su
Keyword(s):  
Compliant Mechanisms ◽  
Large Range ◽  
Beam Theory ◽  
Simple Approach ◽  
Large Deflections ◽  
Model Approximation ◽  
Significant Challenge ◽  
Body Model ◽  
Compliant Joints ◽  
Optimal Values

Compliant mechanisms achieve motion utilizing deformation of elastic members. However, analysis of compliant mechanisms for large deflections remains a significant challenge. In this paper, a three-spring revolute–prismatic–revolute (RPR) pseudorigid-body (PRB) model for short beams used in soft joints made of elastomer material is presented. These soft joints differ from flexure-based compliant joints in which they demonstrate significant axial elongation effects upon tip loadings. The traditional PRB models based on long thin Euler beams failed to capture this elongation effect. To overcome this difficulty, a model approximation based on the Timoshenko beam theory has been derived. These equations are utilized to calculate the tip deflection for a large range of loading conditions. An optimization process is then carried out to determine the optimal values of the parameters of the PRB model for a large range of tip loads. An example based on a robotic grasper finger is provided to demonstrate how the model can be used in analysis of such a system. This model will provide a simple approach for the analysis of compliant robotic mechanisms.

Development of a 3-Spring Pseudo Rigid Body Model of Compliant Joints for Robotic Applications

2014 ◽  
Author(s):  
Venkatasubramanian Kalpathy Venkiteswaran ◽  
Hai-Jun Su
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Large Range ◽  
Beam Theory ◽  
Beam Model ◽  
Significant Challenge ◽  
Body Model ◽  
Compliant Joints ◽  
Rigid Body Model ◽  
Robotic Applications

Compliant mechanisms achieve motion utilizing deformation of elastic members. However, analysis of compliant mechanisms for large deflections remains a significant challenge. In this paper, we will develop a 3-spring pseudo-rigid-body model for 2D beams that are often used in compliant joints in robots. First, we utilize the Timoshenko beam theory to calculate the tip deflection for a large range of loading conditions. An optimization process is then carried out to calculate the values of the parameters of the PRB model. The errors in the model will be analyzed and compared to the beam model. An example based on a robotic grasper finger is provided to demonstrate how the model can be used in analysis of such a system. This model will provide a much simpler approach for the analysis of compliant robotic mechanisms.

A Simple and Accurate Method for Determining Large Deflections in Compliant Mechanisms Subjected to End Forces and Moments

1998 ◽  
Vol 120 (3) ◽  
pp. 392-400 ◽  
Author(s):  
A. Saxena ◽  
S. N. Kramer
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Elliptic Integral ◽  
Beam Equation ◽  
Large Deflections ◽  
Euler Beam ◽  
Body Model ◽  
Rigid Body Model ◽  
Analysis And Synthesis

Compliant members in flexible link mechanisms undergo large deflections when subjected to external loads. Because of this fact, traditional methods of deflection analysis do not apply. Since the nonlinearities introduced by these large deflections make the system comprising such members difficult to solve, parametric deflection approximations are deemed helpful in the analysis and synthesis of compliant mechanisms. This is accomplished by representing the compliant mechanism as a pseudo-rigid-body model. A wealth of analysis and synthesis techniques available for rigid-body mechanisms thus become amenable to the design of compliant mechanisms. In this paper, a pseudo-rigid-body model is developed and solved for the tip deflection of flexible beams for combined end loads. A numerical integration technique using quadrature formulae has been employed to solve the large deflection Bernoulli-Euler beam equation for the tip deflection. Implementation of this scheme is simpler than the elliptic integral formulation and provides very accurate results. An example for the synthesis of a compliant mechanism using the proposed model is also presented.

A Simple and Accurate Method for Determining Large Deflections in Complaint Mechanisms Subjected to End Forces and Moments

1998 ◽  
Author(s):  
A. Saxena ◽  
Steven N. Kramer
Keyword(s):  
Rigid Body ◽  
Numerical Integration ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Beam Equation ◽  
Integration Scheme ◽  
Large Deflections ◽  
Body Model ◽  
Rigid Body Model ◽  
Analysis And Synthesis

Abstract Compliant members in flexible link mechanisms undergo large deflections when subjected to external loads for which, traditional methods of deflection analysis do not apply Nonlinearities introduced by these large deflections make the system comprising such members difficult to solve Parametric deflection approximations are then deemed helpful in the analysis and synthesis of compliant mechanisms This is accomplished by seeking the pseudo-rigid-body model representation of the compliant mechanism A wealth of analysis and synthesis techniques available for rigid-body mechanisms thus become amenable to the design of compliant mechanisms In this paper, a pseudo-rigid-body model is developed and solved for the tip deflection of flexible beams for combined end loads with positive end moments A numerical integration technique using quadrature formulae has been employed to solve the nonlinear Bernoulli-Euler beam equation for the tip deflection Implementation of this scheme is relatively simpler than the elliptic integral formulation and provides nearly accurate results Results of the numerical integration scheme are compared with the beam finite element analysis An example for the synthesis of a compliant mechanism using the proposed model is also presented.

The Compliant A-Arm Suspension

Aerospace ◽  
2003 ◽  
Author(s):  
Timothy Allred ◽  
Larry L. Howell ◽  
Spencer P. Magleby ◽  
Robert H. Todd
Keyword(s):  
Compliant Mechanisms ◽  
Commercial Application ◽  
Leaf Spring ◽  
Large Deflections ◽  
Element Analysis ◽  
Performance Variables ◽  
Body Model ◽  
Small Deflection ◽  
Rigid Body Model ◽  
Depth Study

The use compliant mechanisms in a suspension system has been demonstrated with leaf spring mechanisms. In this research a novel compliant configuration called the Compliant A-Arm (C-A-Arm) suspension is selected for in-depth study. Closed-from equations are derived for linear small-deflection stiffness equations. Large deflections are analyzed using finite element analysis. A pseudo-rigid-body model is developed to approximate mechanism deflections and stiffness for large deflections. The results suggest that the C-A-Arm configuration may be a viable suspension alternative for future commercial application. In addition, this configuration offers a number of performance variables that could be the basis for an active control system. This paper represents a necessary first step in modeling this new configuration.

Dynamic Modeling of Compliant Mechanisms Based on 2R Pseudo-Rigid-Body Model

2012 ◽  
Vol 163 ◽  
pp. 277-280 ◽  
Author(s):  
Wen Jing Wang ◽  
Shu Sheng Bi ◽  
Li Ge Zhang
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Modeling ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Large Deflections ◽  
Flexible Link ◽  
Flexible Links ◽  
Body Model ◽  
Rigid Body Model ◽  
New Type

Compliant mechanism is a kind of new type mechanism and its analysis is very complex because flexible links often under large deflections which introduce geometry nonlinearities. A new model (2R PRBM) can simulate accurately both the deflection path and angle of the flexible link. A new dynamic model of compliant mechanism is developed using the 2R PRBM. The dynamic equation of planar compliant mechanism is derived. The dynamic analysis on the natural frequency of compliant mechanism is obtained in the example of a planar compliant parallel-guiding mechanism. The numerical results show the advantage of the proposed method for the dynamic analysis of compliant mechanisms.

A Family of Dual-Segment Compliant Joints Suitable for Use as Surrogate Folds

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Isaac L. Delimont ◽  
Spencer P. Magleby ◽  
Larry L. Howell
Keyword(s):  
Closed Form ◽  
Compliant Mechanisms ◽  
Large Deflections ◽  
Closed Form Solutions ◽  
Compliant Joints

Origami-inspired design is an emerging field capable of producing compact and efficient designs. The object of a surrogate fold is to provide a foldlike motion in a nonpaper material without undergoing yielding. Compliant mechanisms provide a means to achieve these objectives as large deflections are achieved. The purpose of this paper is to present a continuum of compliant joints capable of achieving motions not currently available with existing compliant joints. A series of compliant joints are presented in which the joint can be designed to allow or resist a variety of secondary motions. Closed-form solutions are presented for these compliant joints.

The Mixed-Body Model: A Method for Predicting Large Deflections in Stepped Cantilever Beams

2021 ◽  
pp. 1-18
Author(s):  
Brandon Sargent ◽  
Collin Ynchausti ◽  
Todd G Nelson ◽  
Larry L Howell
Keyword(s):  
Large Deflections ◽  
Cantilever Beams ◽  
Element Analysis ◽  
Body Model ◽  
Minimal Error ◽  
Small Deflection ◽  
Rigid Body Model ◽  
Expected Values ◽  
Deflection Theory ◽  
Sample Set

Abstract This paper presents a method for predicting endpoint coordinates, stress, and force to deflect stepped cantilever beams under large deflections. This method, the Mixed-Body Model or MBM, combines small deflection theory and the Pseudo-Rigid-Body Model for large deflections. To analyze the efficacy of the model, the MBM is compared to a model that assumes the first step in the beam to be rigid, to finite element analysis, and to the numerical boundary value solution over a large sample set of loading conditions, geometries, and material properties. The model was also compared to physical prototypes. In all cases, the MBM agrees well with expected values. Optimization of the MBM parameters yielded increased agreement, leading to average errors of <0.01 to 3%. The model provides a simple, quick solution with minimal error that can be particularly helpful in design.

Evaluation of Equivalent Spring Stiffness for Use in a Pseudo-Rigid-Body Model of Large-Deflection Compliant Mechanisms

1994 ◽  
Author(s):  
Larry L. Howell ◽  
Ashok Midha
Keyword(s):  
Rigid Body ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Spring Stiffness ◽  
Model Concept ◽  
Analysis And Design ◽  
Body Model ◽  
Rigid Body Model ◽  
Body Joints

Abstract Compliant mechanisms gain some or all of their mobility from the flexibility of their members rather than from rigid-body joints only. More efficient and usable analysis and design techniques are needed before the advantages of compliant mechanisms can be fully utilized. In an earlier work, a pseudo-rigid-body model concept, corresponding to an end-loaded geometrically nonlinear, large-deflection beam, was developed to help fulfill this need. In this paper, the pseudo-rigid-body equivalent spring stiffness is investigated and new modeling equations are proposed. The result is a simplified method of modeling the force/deflection relationships of large-deflection members in compliant mechanisms. Flexible segments which maintain a constant end angle are discussed, and an example mechanism is analyzed. The resulting models are valuable in the visualization of the motion of large-deflection systems, as well as the quick and efficient evaluation and optimization of compliant mechanism designs.

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.

Compliant Pantographs via the Pseudo-Rigid-Body Model

1998 ◽  
Author(s):  
Andrew J. Nielson ◽  
Larry L. Howell
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Test Results ◽  
Rigid Link ◽  
Body Model ◽  
Design Flexibility ◽  
Model Predictions ◽  
Rigid Body Model ◽  
Classical Mechanism

Abstract This paper uses a familiar classical mechanism, the pantograph, to demonstrate the utility of the pseudo-rigid-body model in the design of compliant mechanisms to replace rigid-link mechanisms, and to illustrate the advantages and limitations of the resulting compliant mechanisms. To demonstrate the increase in design flexibility, three different compliant mechanism configurations were developed for a single corresponding rigid-link mechanism. The rigid-link pantograph consisted of six links and seven joints, while the corresponding compliant mechanisms had no more than two links and three joints (a reduction of at least four links and four joints). A fourth compliant pantograph, corresponding to a rhomboid pantograph, was also designed and tested. The test results showed that the pseudo-rigid-body model predictions were accurate over a large range, and the mechanisms had displacement characteristics of rigid-link mechanisms in that range. The limitations of the compliant mechanisms included reduced range compared to their rigid-link counterparts. Also, the force-deflection characteristics were predicted by the pseudo-rigid-body model, but they did not resemble those for a rigid-link pantograph because of the energy storage in the flexible segments.

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