  The mathematical perspective for creating centered trochoids (through a solid
rule that is based on the pure rolling a circle along another circle) is
violated and changed it to a novel vision which is based on the combination of
rolling and sliding motions of a circle along another circle! In this new
vision we have not to define a centered trochoid as a path that is swept by an
attached point to a pure rolling circle along another circle. Instead, a
centered trochoid can be defined as a path that is swept by a definite point on
the circumference of a rolling and sliding circle along another one! In this
article we present two different methods for implement a definite combination
of sliding and rolling motions for a circle along another one in order to make
a simple experimental simulation to create centered trochoids and co-centered
ellipses. In our novel mathematical vision not only, the physical concepts are
playing basic role but also one can deduce the parametric equations of centered
trochoids and ellipses on the bases of rolling and sliding motions. In this
perspective, an ellipse can be visualized as a closed plane curve that can be
generated through a definite combination of rolling and sliding motions due to
two co-polarized rotational motions with different commensurable angular
frequencies! All the above subjects can be implemented with the help of Virtual
Rotating Circles Technique (VRCT) by an innovative device that we have named it
Mechanical Oscilloscope (MO). Although the function of our device is
independent from any electronic devices, but we can create these geometrical
objects on the bases of functional operation of (MO) with the help of computer.
This article establishes a strong link between mathematical vision and
meaningful physical concepts.
