﻿ Qualitative force propagation analysis
Qualitative Representation   Qualitative force propagation analysis

## Qualitative force propagation analysis   (written by Michał Zawidzki)

The qualitative propagation of force (or motion) analysis consists in investigating how a force acting upon an object is distributed over the whole structure of objects our object in consideration is a part of.

There are several approaches to this problem present on the market. One of them, presented by Nielsen in (Nielsen 1988), is to consider objects arranged in the so-called kinematic chains. Two objects which are in contact with each other form a kinematic pair. A closure of the relation of kinematic pair is called a kinematic chain. If there is an external force acting on an object in a kinematics chain, this force will then be distributed to other objects in that chain. There are further questions that need to be addressed, firstly: how will a motion of an object affect another object; secondly: what kind of motion of one object will affect other objects. Nielsen describes two types of motion: translational and rotational. In order to determine how an object will move and whether it will have any effect on other objects one must first eliminate the constrained motions (i.e. motions which are impossible due to some constraints, e.g., a wall) and then apply the motion transfer.

In (Pu 1989) Pu considers the "flow" of force and velocity through a structure consisting of several blocks. She analyses the propagation of force for a dynamical model in terms of a simple input-output mechanism. For a structure consisting of three blocks standing next to each other if we act with a certain force on the first block it will then act with another force on the second one and so on. The incoming force is the "force-in" which is transformed into the "force-out" which in turn acts on the second block as the "force-in" again. Hence for a structure consisting of connected blocks the force flows through the structure.

In (Wałęga et al. 2016) Wałęga et al. introduce the so-called Horizontal Impact algorithm which our follows both of the above approaches - Nielsen's and Pu's - extending them to more general cases (e.g. when an object pushes two other objects in a given direction). It differentiates the scale of force propagation from one object to another depending on their mutual spatial arrangement (e.g., the latter lies on the former or supports it from below).

## References

1. Nielsen, P. E. (1988). A Qualitative Approach to Rigid Body Mechanics. PhD thesis, Champaign, IL, USA. AAI8908788.
2. Pu, P. (1989). Simulating both dynamic and kinematic behaviors of mechanisms. In Proceedings of the Third Workshop on Qualitative Reasoning, 1–13, Stanford, CA, USA.
3. Wałega, P.A., Zawidzki, M., & Lechowski, T. (2016). Qualitative physics in angry birds. IEEE Transactions on Computational Intelligence and AI in Games, 8(2), 152–165.