Swept volumes via spacetime numerical continuation

2021 ◽  
Vol 40 (4) ◽  
pp. 1-11
Author(s):  
Silvia Sellán ◽  
Noam Aigerman ◽  
Alec Jacobson
Keyword(s):  
Numerical Continuation ◽  
Swept Volumes

Swept volumes via spacetime numerical continuation

2021 ◽  
Vol 40 (4) ◽  
pp. 1-11
Author(s):  
Silvia Sellán ◽  
Noam Aigerman ◽  
Alec Jacobson
Keyword(s):  
Numerical Continuation ◽  
Swept Volumes

Online motion generation using accumulated swept volumes

2020 ◽  
pp. 1-13
Author(s):  
Rui Zhu ◽  
Kotaro Nagahama ◽  
Keisuke Takeshita ◽  
Kimitoshi Yamazaki
Keyword(s):  
Motion Generation ◽  
Swept Volumes

scholarly journals Two dimensionless parameters and a mechanical analogue for the HKB model of motor coordination

2021 ◽  
Author(s):  
J. F. Cass ◽  
S. J. Hogan
Keyword(s):  
Motor Coordination ◽  
Nonlinear Damping ◽  
Numerical Continuation ◽  
Arbitrary Parameter ◽  
Relevant Parameter ◽  
Coupling Coefficients ◽  
Dimensionless Parameters ◽  
Biologically Relevant ◽  
Mechanical Analogue ◽  
Partner Interaction

AbstractThe widely cited Haken–Kelso–Bunz (HKB) model of motor coordination is used in an enormous range of applications. In this paper, we show analytically that the weakly damped, weakly coupled HKB model of two oscillators depends on only two dimensionless parameters; the ratio of the linear damping coefficient and the linear coupling coefficient and the ratio of the combined nonlinear damping coefficients and the combined nonlinear coupling coefficients. We illustrate our results with a mechanical analogue. We use our analytic results to predict behaviours in arbitrary parameter regimes and show how this led us to explain and extend recent numerical continuation results of the full HKB model. The key finding is that the HKB model contains a significant amount of behaviour in biologically relevant parameter regimes not yet observed in experiments or numerical simulations. This observation has implications for the development of virtual partner interaction and the human dynamic clamp, and potentially for the HKB model itself.

scholarly journals Numerical Continuation Analysis of a Dual-sidestay Main Landing Gear Mechanism

2012 ◽  
Author(s):  
James Knowles ◽  
Bernd Krauskopf ◽  
Mark Lowenberg ◽  
Simon Neild ◽  
P. Thota
Keyword(s):  
Landing Gear ◽  
Numerical Continuation ◽  
Gear Mechanism

Dynamics and Performance of a Harmonically Excited Vertical Impact Damper

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Sanjiv Ramachandran ◽  
George Lesieutre
Keyword(s):  
Loss Factor ◽  
Vertical Direction ◽  
Theoretical Models ◽  
Coefficient Of Restitution ◽  
Numerical Continuation ◽  
Particle Impact ◽  
Impact Damper ◽  
High Loss ◽  
Wide Range ◽  
And Performance

Particle impact dampers (PIDs) have been shown to be effective in vibration damping. However, our understanding of such dampers is still limited, based on the theoretical models existing today. Predicting the performance of the PID is an important problem, which needs to be investigated more thoroughly. This research seeks to understand the dynamics of a PID as well as those parameters which govern its behavior. The system investigated is a particle impact damper with a ceiling, under the influence of gravity. The base is harmonically excited in the vertical direction. A two-dimensional discrete map is obtained, wherein the variables at one impact uniquely dictate the variables at the next impact. This map is solved using a numerical continuation procedure. Periodic impact motions and “irregular” motions are observed. The effects of various parameters such as the gap clearance, coefficient of restitution, and the base acceleration are analyzed. The dependence of the effective damping loss factor on these parameters is also studied. The loss factor results indicate peak damping for certain combinations of parameters. These combinations of parameters correspond to a region in parameter space where two-impacts-per-cycle motions are observed over a wide range of nondimensional base accelerations. The value of the nondimensional acceleration at which the onset of two-impacts-per-cycle solutions occurs depends on the nondimensional gap clearance and the coefficient of restitution. The range of nondimensional gap clearances over which two-impacts-per-cycle solutions are observed increases as the coefficient of restitution increases. In the regime of two-impacts-per-cycle solutions, the value of nondimensional base acceleration corresponding to onset of these solutions initially decreases and then increases with increasing nondimensional gap clearance. As the two-impacts-per-cycle solutions are associated with high loss factors that are relatively insensitive to changing conditions, they are of great interest to the designer.

SHARP: A System for Haptic Assembly and Realistic Prototyping

2006 ◽  
Author(s):  
Abhishek Seth ◽  
Hai-Jun Su ◽  
Judy M. Vance
Keyword(s):  
Virtual Environments ◽  
Virtual Prototyping ◽  
Mechanical Assembly ◽  
Swept Volumes ◽  
Physically Based ◽  
Product Design Process ◽  
Costly Product ◽  
Easy Integration ◽  
Realization Process ◽  
Product Realization

Virtual Reality (VR) technology holds promise as a virtual prototyping tool for mechanical assembly; however, several developmental challenges still need to be addressed before virtual prototyping applications can successfully be integrated into the product realization process. This paper describes the development of SHARP (System for Haptic Assembly & Realistic Prototyping), a portable VR interface for virtual assembly. SHARP uses physically-based modeling for simulating realistic part-to-part and hand-to-part interactions in virtual environments. A dual handed haptic interface for realistic part interaction using the PHANToM® haptic devices is presented. The capability of creating subassemblies enhances the application’s ability to handle a wide variety of assembly scenarios. Swept volumes are implemented for addressing maintainability issues and a network module is added for communicating with different VR systems at dispersed geographic locations. Support for various types of VR systems allows an easy integration of SHARP into the product realization process resulting in faster product development, faster identification of assembly and design issues and a more efficient and less costly product design process.

LOCAL AND GLOBAL BIFURCATIONS IN THREE-DIMENSIONAL, CONTINUOUS, PIECEWISE SMOOTH MAPS

2011 ◽  
Vol 21 (06) ◽  
pp. 1617-1636 ◽  
Author(s):  
SOMA DE ◽  
PARTHA SHARATHI DUTTA ◽  
SOUMITRO BANERJEE ◽  
AKHIL RANJAN ROY
Keyword(s):  
Three Dimensional ◽  
Global Bifurcation ◽  
Period Doubling ◽  
Piecewise Smooth ◽  
Numerical Continuation ◽  
Homoclinic Tangency ◽  
Global Dynamics ◽  
Global Bifurcations ◽  
Border Collision Bifurcation ◽  
Smooth Map

In this work, we study the dynamics of a three-dimensional, continuous, piecewise smooth map. Much of the nontrivial dynamics of this map occur when its fixed point or periodic orbit hits the switching manifold resulting in the so-called border collision bifurcation. We study the local and global bifurcation phenomena resulting from such borderline collisions. The conditions for the occurrence of nonsmooth period-doubling, saddle-node, and Neimark–Sacker bifurcations are derived. We show that dangerous border collision bifurcation can also occur in this map. Global bifurcations arise in connection with the occurrence of nonsmooth Neimark–Sacker bifurcation by which a spiral attractor turns into a saddle focus. The global dynamics are systematically explored through the computation of resonance tongues and numerical continuation of mode-locked invariant circles. We demonstrate the transition to chaos through the breakdown of mode-locked torus by degenerate period-doubling bifurcation, homoclinic tangency, etc. We show that in this map a mode-locked torus can be transformed into a quasiperiodic torus if there is no global bifurcation.

Generating Swept Volumes With Instantaneous Screw Axes

1994 ◽  
Author(s):  
Zeng-Jia Hu ◽  
Zhi-Kui Ling
Keyword(s):  
Moving Object ◽  
Ruled Surfaces ◽  
Screw Axis ◽  
Spherical Surfaces ◽  
Swept Volumes ◽  
Instantaneous Screw Axis ◽  
Swept Volume ◽  
Instantaneous Screw ◽  
Plane Polygon ◽  
Boundary Surfaces

Abstract The instantaneous screw axis is used in the generation of the swept volume of a moving object. The envelope theory is used to determine the boundary surfaces of the swept volume. Specifically, the envelope surfaces generated by a plane polygon, cylindrical and spherical surfaces are presented. Furthermore, the ruled surfaces generated by edges of the moving object are discussed.

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