Closure to “Discussions of ‘Dimensionless Parameters for Helical Compression Springs’” (1960, ASME J. Eng. Ind., 82, p. 442)

1960 ◽  
Vol 82 (4) ◽  
pp. 443-443
Author(s):  
R. J. Erisman
Keyword(s):  
Dimensionless Parameters ◽  
Compression Springs

Dimensionless Parameters for Helical Compression Springs

1960 ◽  
Vol 82 (4) ◽  
pp. 439-442 ◽  
Author(s):  
R. J. Erisman
Keyword(s):  
Complex Variables ◽  
Trial And Error ◽  
Entire Space ◽  
Dimensionless Parameters ◽  
Error Process ◽  
Compression Springs ◽  
System Of Parameters ◽  
Outside Diameter

Spring design, in many instances, is still a trial-and-error process. The underlying reason is the large number of complex variables which must be related to the allotted space which the spring will occupy and to the desired loads throughout the working range. This paper presents a system of parameters which enables the spring designer to graphically portray these variables for a given problem. Derivations are based on the total number of coils as well as the outside diameter which accurately defines the entire space required for the spring. Charts are presented for springs with two dead coils and a torsion modulus of 11,500,000 psi.

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.

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