Structures With Multiple Rigid Configurations Due to Prestress and Unilateral Contacts

2021 ◽  
Author(s):  
Charles Dorn ◽  
Yang Li ◽  
Sergio Pellegrino
Keyword(s):  
Degree Of Freedom ◽  
Multiple Equilibrium ◽  
Multiple Target ◽  
Unilateral Constraints ◽  
Equilibrium Configurations ◽  
Unilateral Contacts ◽  
Reaction Forces ◽  
Rf Antenna ◽  
Four Bar Linkage ◽  
Multiple Configurations

Abstract This paper presents structures with multiple equilibrium configurations arising from the combination of a state of prestress and unilateral contacts. A design problem is posed where preloaded elastic springs and unilateral constraints are embedded throughout a mechanism. The spring parameters are designed such that multiple target configurations are immobilized due to contact. In each of these configurations, the spring forces maintain compressive reaction forces, immobilizing the structure. Each immobilized configuration can rigidly resist perturbation forces up to some finite magnitude where contact is lost. Hence, this case of multiple configurations in equilibrium due to the combination of prestress and contact is referred to as multi-configuration rigidity. Two examples of structures exhibiting multi-configuration rigidity are presented. First, a four bar linkage with a single kinematic degree of freedom is used to introduce the concept. In the context of the linkage, multi-configuration rigidity is compared to multi-stability, exhibiting the key differences between the two concepts. Then, a 24-degree-of-freedom kirigami surface is presented that can morph between flat and spherical configurations, motivated by RF antenna applications. By embedding torsional springs and fold angle stops throughout the structure, flat and spherical configurations are made rigid. Actuation between the configurations can easily be achieved by snapping the structure between the rigid configurations.

Design of Structures With Multiple Equilibrium Configurations

2018 ◽  
Author(s):  
Yang Li ◽  
Sergio Pellegrino
Keyword(s):  
Multiple Equilibrium ◽  
Design Parameters ◽  
Future Research ◽  
Equilibrium Constraints ◽  
Complex Problems ◽  
Equilibrium Configurations ◽  
Four Bar Linkage ◽  
Stable Structures

Being able to design structures with multiple equilibrium configurations is the basis for the design of multi-stable structures, which are of interest for future research on multi-configuration structures that require ‘simple’ actuation schemes. It is already known that adding elastic springs to a rigid mechanism can create structures with multiple equilibrium configurations. The spring properties, such as their rest positions, can be taken as design parameters that can be used to achieve specific equilibrium configurations of the structure. This paper provides a linearized formulation for the equilibrium constraints that can be solved for the rest positions of the springs. This method allows the design of specific equilibrium configurations. It can also handle more complex problems and is easier to solve in comparison to existent techniques. An example design of a four-bar linkage that has 5 equilibrium configurations is presented.

Synthesis of Compliant Mechanisms With Specified Equilibrium Positions

2005 ◽  
Author(s):  
Hai-Jun Su ◽  
J. Michael McCarthy
Keyword(s):  
Compliant Mechanisms ◽  
Equilibrium Constraints ◽  
Equilibrium Equations ◽  
Equilibrium Configurations ◽  
Form Design ◽  
Design Requirements ◽  
Synthesis Procedure ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
Sine And Cosine Functions

This paper presents a synthesis procedure for a compliant four-bar linkage with three specified equilibrium configurations. The finite position synthesis equations are combined with equilibrium constraints at the flexure pivots to form design equations. These equations are simplified by modeling the joint angle variables in the equilibrium equations using sine and cosine functions. Solutions to these design equations were computed using a polynomial homotopy solver. In order to provide a design specification, we first compute the six equilibrium configurations of a known compliant four-bar mechanism. We use these results as design requirements to synthesize a compliant four-bar. The solver obtained eight real solutions which we refined using a Newton-Raphson technique. A numerical example is provided to verify the design methodology.

Synthesis, Design, and Prototyping of a Planar Three Degree-of-Freedom Reactionless Parallel Mechanism

2004 ◽  
Vol 126 (6) ◽  
pp. 992-999 ◽  
Author(s):  
Simon Foucault ◽  
Cle´ment M. Gosselin
Keyword(s):  
Parallel Mechanism ◽  
Degree Of Freedom ◽  
Numerical Verification ◽  
Dynamic Balancing ◽  
Synthesis Design ◽  
Reaction Forces ◽  
Three Degree Of Freedom

This paper addresses the dynamic balancing of a planar three-degree-of-freedom parallel mechanism. A mechanism is said to be dynamically balanced if, for any motion of the mechanism, the reaction forces and torques at the base are identically equal to zero, at all times. The proposed mechanism is based on legs consisting of five-bar parallelogram linkages. The balancing equations are first obtained. Then, optimization is used in order to minimize the mass and inertia of the moving links. Finally, a numerical verification of the dynamic balancing is provided and the prototype is presented.

Static Balancing of Tensegrity Mechanisms

2006 ◽  
Vol 129 (3) ◽  
pp. 295-300 ◽  
Author(s):  
Marc Arsenault ◽  
Clément M. Gosselin
Keyword(s):  
Degree Of Freedom ◽  
Static Balancing ◽  
Equilibrium Configurations ◽  
Balancing Conditions ◽  
Three Degree Of Freedom

The computation of the equilibrium configurations of tensegrity mechanisms is often a very tedious task even for relatively simple architectures. However, it has been observed that the complexity of this problem is significantly reduced when gravitational loads are compensated with the use of static balancing techniques. In this work, the general static balancing conditions are adapted for the case of tensegrity mechanisms. Afterward, the modified conditions are applied to two new spatial three-degree-of-freedom tensegrity mechanisms.

A Unit-Consistent Error Measure for Multibody Systems With Unilateral Constraints

2019 ◽  
Vol 14 (5) ◽  
Author(s):  
Andreas Enzenhöfer ◽  
Albert Peiret ◽  
Marek Teichmann ◽  
József Kövecses
Keyword(s):  
Multibody Systems ◽  
Reference Trajectory ◽  
Unilateral Constraints ◽  
Error Measure ◽  
Energy Error ◽  
Error Measures ◽  
Unilateral Contacts ◽  
Mixed Linear Complementarity Problem ◽  
Consistent Error ◽  
Real Time Simulations

Modeling multibody systems subject to unilateral contacts and friction efficiently is challenging, and dynamic formulations based on the mixed linear complementarity problem (MLCP) are commonly used for this purpose. The accuracy of the MLCP solution method can be evaluated by determining the error introduced by it. In this paper, we find that commonly used MLCP error measures suffer from unit inconsistency leading to the error lacking any physical meaning. We propose a unit-consistent error measure, which computes energy error components for each constraint dependent on the inverse effective mass and compliance. It is shown by means of a simple example that the unit consistency issue does not occur using this proposed error measure. Simulation results confirm that the error decreases with convergence toward the solution. If a pivoting algorithm does not find a solution of the MLCP due to an iteration limit, e.g., in real-time simulations, choosing the result with the least error can reduce the risk of simulation instabilities and deviation from the reference trajectory.

Static Balancing of Tensegrity Mechanisms

2005 ◽  
Author(s):  
Marc Arsenault ◽  
Cle´ment M. Gosselin
Keyword(s):  
Degree Of Freedom ◽  
Static Balancing ◽  
Equilibrium Configurations ◽  
Balancing Conditions ◽  
Three Degree Of Freedom

The computation of the equilibrium configurations of tensegrity mechanisms is often a very tedious task even for relatively simple architectures. However, it has been observed that the complexity of this problem is significantly reduced when gravitational loads are compensated with the use of static balancing techniques. In this work, the general static balancing conditions are adapted for the case of tensegrity mechanisms. Afterwards, the modified conditions are applied to two new spatial three-degree-of-freedom tensegrity mechanisms.

scholarly journals Single degree of freedom everting ring linkages with nonorientable topology

2018 ◽  
Vol 116 (1) ◽  
pp. 90-95 ◽  
Author(s):  
Johannes Schönke ◽  
Eliot Fried
Keyword(s):  
Twist Angle ◽  
Rigid Bodies ◽  
Internal Degree ◽  
Degree Of Freedom ◽  
Planar Mechanisms ◽  
Single Degree Of Freedom ◽  
Robotic Arms ◽  
Ring Molecules ◽  
Internal Degree Of Freedom ◽  
Four Bar Linkage

Linkages are assemblies of rigid bodies connected through joints. They serve as the basis for force- and movement-managing devices ranging from ordinary pliers to high-precision robotic arms. Aside from planar mechanisms, like the well-known four-bar linkage, only a few linkages with a single internal degree of freedom—meaning that they can change shape in only one way and may thus be easily controlled—have been known to date. Here, we present “Möbius kaleidocycles,” a previously undiscovered class of single-internal degree of freedom ring linkages containing nontrivial examples of spatially underconstrained mechanisms. A Möbius kaleidocycle is made from seven or more identical links joined by revolute hinges. These links dictate a specific twist angle between neighboring hinges, and the hinge orientations induce a nonorientable topology equivalent to the topology of a3π-twist Möbius band. Apart from having many technological applications, including perhaps the design of organic ring molecules with peculiar electronic properties, Möbius kaleidocycles raise fundamental questions about geometry, topology, and the limitations of mobility for closed loop linkages.

Stability of Doubly Periodic Deformed Configurations of Plates and Shallow Shells

1970 ◽  
Vol 37 (3) ◽  
pp. 641-650 ◽  
Author(s):  
C. S. Hsu ◽  
S. S. Lee
Keyword(s):  
Stability Analysis ◽  
Nonlinear Analysis ◽  
Large Deflection ◽  
Multiple Equilibrium ◽  
Jump Phenomenon ◽  
Periodic Surface ◽  
Shallow Shells ◽  
Equilibrium Configurations

Presented here is a nonlinear analysis of infinite plates and shallow shells, subjected to doubly periodic surface loadings. The drastically different behaviors predicted by the linear and the nonlinear theories are analyzed and discussed. It turns out that the transition from the small to the large deflection behavior involves nonlinear bifurcation and the existence of multiple equilibrium configurations, and it entails the question of stability. Seen in this light, it is easy to explain various features special to problems in this class, including the jump phenomenon. From the viewpoint of stability analysis, this class of problems is distinct and interesting in that the perturbations which can lead to instability have actually a higher degree of symmetry than the unperturbed configurations.

Instantaneous motion and constraint analysis of Bennett linkage

2014 ◽  
Vol 230 (3) ◽  
pp. 379-391 ◽  
Author(s):  
Xiang Liu ◽  
Jing-Shan Zhao ◽  
Zhi-Jing Feng
Keyword(s):  
Analytical Method ◽  
Degree Of Freedom ◽  
Helical Motion ◽  
Mobility Analysis ◽  
Interesting Phenomenon ◽  
Constraint Analysis ◽  
Four Bar Linkage

Bennett linkage is a well-known spatial four-bar linkage with one degree-of-freedom (DOF). Although mobility analysis of Bennett linkage has been carried out by many researchers, the type, direction and location of the instantaneous motion are seldom discussed. This paper focuses on investigating the full mobility information of Bennett linkage by using analytical method for mobility, and then addresses its extending application to a Bennett-based six-bar linkage. The result demonstrates that the instantaneous motion of Bennett linkage is always a helical motion. However, the location, direction and pitch of the helical motion are changing related to different configurations. An interesting phenomenon is that the direction of helical motion will reverse suddenly when passing through the configuration that the axes of these four links keep collinear. As an extending application, a Bennett-based six-bar linkage is discussed and its peculiar mobility is an instantaneous rotation without considering the bifurcation.

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