In this paper, a pseudorigid-body (PRB) 3R model, which consists of four rigid links joined by three revolute joints and three torsion springs, is proposed for approximating the deflection of a cantilever beam subject to a general tip load. The large deflection beam equations are solved through numerical integration. A comprehensive atlas of the tip deflection for various load modes is obtained. A three-dimensional search routine has been developed to find the optimal set of characteristic radius factors and spring stiffness of the PRB 3R model. Detailed error analysis has been done by comparing with the precomputed tip deflection atlas. Our results show that the approximation error is much less than that of the conventional PBR 1R model. To demonstrate the use of the PRB 3R model, a compliant four-bar linkage is studied and verified by a numerical example. The result shows a maximum tip deflection error of 1.2% compared with the finite element analysis model. The benefits of the PRB 3R model include that (a) the model parameters are independent of external loads, (b) the approximation error is relatively small for even large deflection beams, and (c) the derived kinematic and static constraint equations are simpler to solve compared with the finite element model.
Skip Nav Destination
e-mail: haijun@umbc.edu
Article navigation
Research Papers
A Pseudorigid-Body 3R Model for Determining Large Deflection of Cantilever Beams Subject to Tip Loads
Hai-Jun Su
Hai-Jun Su
Department of Mechanical Engineering,
e-mail: haijun@umbc.edu
University of Maryland
, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250
Search for other works by this author on:
Hai-Jun Su
Department of Mechanical Engineering,
University of Maryland
, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250e-mail: haijun@umbc.edu
J. Mechanisms Robotics. May 2009, 1(2): 021008 (9 pages)
Published Online: January 7, 2009
Article history
Received:
April 8, 2008
Revised:
November 1, 2008
Published:
January 7, 2009
Citation
Su, H. (January 7, 2009). "A Pseudorigid-Body 3R Model for Determining Large Deflection of Cantilever Beams Subject to Tip Loads." ASME. J. Mechanisms Robotics. May 2009; 1(2): 021008. https://doi.org/10.1115/1.3046148
Download citation file:
Get Email Alerts
2024 Reviewers
J. Mechanisms Robotics
Inverse Design of Three-Dimensional Variable Curvature Pneumatic Soft Actuators
J. Mechanisms Robotics (July 2025)
Exact Solutions of the Mixed Motion and Path Synthesis Problem for Four-Bar Linkages
J. Mechanisms Robotics (July 2025)
Related Articles
Modeling of a One-Sided Bonded and Rigid Constraint Using Beam Theory
J. Appl. Mech (May,2008)
An Accurate Singularity-Free Formulation of a Three-Dimensional Curved Euler–Bernoulli Beam for Flexible Multibody Dynamic Analysis
J. Vib. Acoust (October,2016)
A Method for Calculating and Continuing Static Solutions for Flexible Multibody Systems
J. Comput. Nonlinear Dynam (July,2018)
Compliant Wireform Mechanisms
J. Mech. Des (December,2008)
Related Proceedings Papers
Related Chapters
Mechanics of Long Beam Columns
Mechanics of Drillstrings and Marine Risers
Stress Concentration Factors in Multiple Row Joints
Structural Shear Joints: Analyses, Properties and Design for Repeat Loading
Experimental Research of Dynamic Parameters of Stranded-Wire Helical Springs under Impact Load
International Conference on Mechanical Engineering and Technology (ICMET-London 2011)