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The Mechanism World

Just as many discrete envisionment programs operate in the domain of circuits (either electronic or hydraulic), many qualitative spatial reasoning programs operate in the ``Mechanism World'', or ``Machine World''. This domain involves analysing motion in systems of rigid mechanical components. The interaction between components includes relative motion, mutual constraint, and transmission of kinetic energy.

The reasons that this domain is popular appear to be firstly that it has been thoroughly analysed at a theoretical level (in mechanical engineering), and secondly that behaviour of mechanical devices is usually simple and consistent - they have been designed with the objective of achieving predictable and repeatable motion.

Two systems for the qualitative analysis of mechanisms are those produced by Stanfill [Sta83a], and Joskowicz [Jos87]. Stanfill's ``Mack'' system accepts a geometric representation of a simple machine, and applies rules in solid geometry, mechanics, and pneumatics, to produce a qualitative description of the machine's behaviour. Typical machines analysed by Mack are pistons and cylindrical bearings. Mack operates by building successive models of the system in terms of pneumatics, forces, acceleration, and process, with the final process model being an expression in the form of Forbus' qualitative process theory; it relates motions to pressures and to other motions. The spatial analysis component of this sytem uses geometric techniques, and it is only the more abstract levels that are expressed in qualitative form.

Joskowicz describes a system which reasons about kinematic chains. A kinematic chain is a series of kinematic pairs. A kinematic pair is a mechanical device which transmits kinetic energy, such as a pair of cogs, or a belt and pulley. Each pair involves two components in contact, with at least one axis of possible relative motion (i.e. they are not rigidly joined). Kinematic pairs can enable the transmission of kinetic energy between components, and they can also provide various types of constraint on the motion of components.

This system initially analyses the possible axes of motion for each pair of components in the chain, using a configuration space derived from a constructive solid geometry description of the components. A qualitative envisionment is then carried out to determine the operation of the whole chain, with kinetic energy being treated as a material that is affected by each kinematic pair. This stage of the analysis is closely related to the techniques used for circuit or fluid flow analysis, and described above. The spatial analysis, however, uses standard geometric techniques for determining configuration space from a CSG description, rather than qualitative methods.

Neither of these two systems operate from first principles in analysing relative motion of a pair of components in contact; instead, they classify each combination of components into a known category. Joskowicz's system uses Reuleaux's 1876 classification of kinematic pairs, for instance.3.6 Faltings considers that this approach lacks power because the system cannot deal with situations that are not represented in its symbol set [Fal86] [Fal87].

Forbus, Faltings and Neilsen describe the application of Forbus' metric diagram and place vocabulary (or MD/PV) approach to the ``mechanism world'' [FNF87]. State is represented in terms of connectivity, or types of contact between objects. The metric diagram provides quantitative information from which one can calculate a configuration space for the component, given constraints on its motion. This configuration space is then subdivided according to contacts that can occur between components. The place vocabulary is created from this information, and qualitative motion can be envisioned in terms of changes in state between these contact configurations. For example, the turning of a ratchet involves state transitions from contact between one gear tooth and the pawl, to a later state of contact with another gear tooth.

The MD/PV model also aims to solve problems involving kinematic chains, and Faltings' goal as described in [Fal86] is to explain the action of a clock after an analysis of individual kinematic pairs within it. An envisionment of motion in a complete mechanism such as this would involve operating on very complex system states that include connectivity information for all components of the mechanism.

Plimmer's study of kinematic chains as found in the analysis of a bicycle [Pli85] makes use of a simple three-valued quantity space in determining direction of motion for bicycle components such as cogs and chains. Causal motion relationships between components are represented explicitly by interaction slots in a functional representation of each component in the kinematic chain. The bicycle analysis system does not include any notion of state, and deals only with a bicycle which is in a ``static'' condition (actually in constant motion, without acceleration or deceleration).

Systems that operate in the ``mechanism world'' all reason about contact between components, and contain only components that have motion constrained by axes or joints, so that there are no more than two degrees of freedom in motion (only one - direction of rotation - in Faltings, Stanfill and Plimmer). The system which I describe in chapter 5 can represent objects moving in free space, as well as objects in contact. The above systems use quantitative geometric techniques to establish fundamental motion constraints from shape description, in particular Lozano-Perez's configuration space method (this is described in [LP83]). The system I describe is interesting in that it derives possible motion from shape using qualitative methods only.

Next: Other Spatial Reasoning Systems Up: Spatial Qualitative Reasoning Previous: The Bouncing Ball World
Alan Blackwell
2000-11-17