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Relational particle mechanics models (RPM's) are useful models for theproblem of time in quantum gravity and other foundational issues in quantumcosmology. Some concrete examples of scalefree RPM's have already been studied,but it is the case with scale that is needed for the semiclassical anddilational internal time approaches to the problem of time. In this paper, Ishow that the scaled RPM's configuration spaces are the cones over thescalefree RPM's configuration spaces, which are spheres in 1-d and complexprojective spaces in 2-d for plain shapes, and these quotiented by Z_2 fororiented shapes. I extend the method of physical interpretation by tessellationof the configuration space and the description in terms of geometricalquantities to the cases with scale and/or orientation. I show that there is anabsence of monopole issues for RPM's and point out a difference between quantumcosmological operator ordering and that used in molecular physics. I use upRPM's freedom of the form of the potential to more closely parallel variouswell-known cosmologies, and begin the investigation of the semiclassicalapproach to the problem of time for such models.

Relational mechanics of shape and scale