Embodiments of the invention move objects throughout two-dimensional and three-dimensional space by using a movement line that is coupled with a plurality of opposing sides of the platform. The movement line is used to control the horizontal axis motion and Z-axis motion of the platform and is designated the horizontal movement line. Displacing a portion of the horizontal movement line allows vertical displacement of the platform to be traversed. There is no need for a complex computer control system since the Z-axis displacement is substantially independent of horizontal movement over a coverage area serviced by the platform. Nested embodiments utilizing one or more rope allow for three-dimensional movement of an object or angular displacement of an object with respect to the vertical axis. A mounting beam for positioning and supporting the Z-axis and horizontal axis motors and visual display element(s) and other optional multimedia devices may also be positioned independently of the platform. In addition, since the line may be commanded from one point, distantly located motors and electrical cables are not required. Many types of useful devices may then be attached to the platform including devices that require external power or devices that possess their own power and are operated via wireless signals.