Force as a flow variable

Abstract

The paper stems from an assessment of the suitability of bond graphs for modelling mechanical systems. Although mathematically rigorous, difficulties arise with intuitive interpretation of bond graphs. The source of the difficulty is the semantics commonly adopted and the way that they relate to traditional interpretations of mechanical system dynamics. Bond graphs represent dynamic systems as energy manipulators with the flow of energy given by the product of two power variables, commonly described as the flow and effort variables. In the mechanical domain, velocity is commonly described as the flow variable, and force as the effort variable. The physical interpretation of mechanical systems and the analogies across systems domains are much improved if force is adopted as the flow variable and the second power variable (i.e. velocity) is called the potential variable. Force can be represented as the flow of a mechanical charge, where the total charge stored in a mass is equal to its momentum. It displays all the properties of a flow variable. Mass is then analogous to electrical capacitance, and mechanical compliance is analogous to electrical inductance.

Mechanical System Modelling of Robot Dynamics Using a Mass/Pulley Model

“…In mechanical systems, velocity V(s) is the across variable and force F(s) is the through variable (i.e. flow variable (Fairlie-Clarke, 1999)). This results in a correspondence between resistance R and damping B, inductance L and spring constant K, and capacitance C and mass M shown in (1-3).…”

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“…Although a number of bond graph papers have appeared in this Journal since its inception [1][2][3][4][5], the bond graph approach is unfamiliar to many and so, in addition to its usual role, this Editorial serves as a tutorial introduction to the bond graph approach. Deeper exposition of bond graphs can be found in textbooks such as references [6 ] to [8].…”

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“…When associated together (multiplied), those two patterns give rise to products (Section 5). For examples in thermodynamics, refer to "Force as a flow variable" by Fairlie-Clarke (1999) and "Analogy theory for a system approach to physical and technical systems" by Hezemans & Geffen (1991); for an example in economics, refer to "A practical guide to trade policy analysis" by Bacchetta et al (2012); and for an example in education, see "Understanding whole numbers" by Nunes and Bryant (2009). cognitive semantics 5 (2019) 201-223 only the character of sensations but also all subsequent associations including diverse forms of expression with natural language among them.…”