  Relational particle mechanics models (RPM's) are useful models for the
problem of time in quantum gravity and other foundational issues in quantum
cosmology. Some concrete examples of scalefree RPM's have already been studied,
but it is the case with scale that is needed for the semiclassical and
dilational internal time approaches to the problem of time. In this paper, I
show that the scaled RPM's configuration spaces are the cones over the
scalefree RPM's configuration spaces, which are spheres in 1-d and complex
projective spaces in 2-d for plain shapes, and these quotiented by Z_2 for
oriented shapes. I extend the method of physical interpretation by tessellation
of the configuration space and the description in terms of geometrical
quantities to the cases with scale and/or orientation. I show that there is an
absence of monopole issues for RPM's and point out a difference between quantum
cosmological operator ordering and that used in molecular physics. I use up
RPM's freedom of the form of the potential to more closely parallel various
well-known cosmologies, and begin the investigation of the semiclassical
approach to the problem of time for such models.
