This post continues the discussion here and here.
Simple motion is “a motion in a straight line, circle or circular arc, or helix”. Since a helix and all other motions are a combination of linear and circular motions, simple motion may be considered as linear or circular motion.
There are two basic measures of simple motion: distance and duration. Linear distance is a length of space. Linear duration is a length of time. Circular distance is an angle of space. Circular duration is an angle of time.
Linear measurements use a measuring rod, and circular measurements use a measuring angle. Other devices that produce the same results may also be used. The convention is to measure distance by linear motion and duration by circular motion, but one could just as well measure distance by circular motion (a measuring wheel) and duration by linear motion (a clock with reciprocating motion).
The linear distance of a linear motion is measured by a measuring rod moving parallel to the linear motion. The linear duration of a linear motion is measured by a measuring rod moving synchronously with the linear motion.
The circular distance of a circular motion is measured by a measuring angle moving in parallel with the circular motion. The circular duration of a circular motion is measured by a measuring angle moving synchronously with the circular motion.
A stopwatch or chronometer is needed to measure time. The continuous motion of a clock provides a convenient source for synchronous measurement but is not necessary to measure time. A clock, calendar, and epoch (starting point) are needed for chronology, which is part of history.
Space is the set of all possible linear and circular distances. Time is the set of all possible linear and circular durations. Mathematically, space and time are metric spaces.
A direction is “the line or course on which something is moving or is aimed to move or along which something is pointing or facing”. A direction angle is the angle made by a given linear motion with a reference linear motion.
A dimension is one of a set of coordinates that are mutually independent or orthogonal. A dimension angle is one of a set of direction angles that are mutually orthogonal. There are three dimension angles in the physical world, so there are three dimensions of distance and duration, that is, of space and time. Since space and time are independent, there are a total of six dimensions of motion for space and time.