An overhead door with height h30 and weight W800lb consists

An overhead door with height h=30 and weight W=800lb, consists of two identical sections hinged at C. The roller at A moves along a horizontal guide, whereas the rollers at B and D, which are midpoints of sections AC and CE, move along a vertical guide. The doors\'s operation is assisted by two identical springs attatched to the horizontally moving rollers (Only one of the two springs is shown). The springs are stetched 0.25 ft when the door is fully open. Determine the minimum value of the spring constant k if the roller at A is to strike the left end of the horizontal guide with a maximum speed of 1.5 ft/s after the door is released from the rest in the fully open position.

Horizontal guide Fully open Vertical guide Fully closed Figure P7.79 Assuming that friction between the rollers and the guide can be neglected, determine the equation (s) of motion of the system

Solution

Overhead doors are not new and are seen frequently in buildings such as homes, automotive shops, barns, aircraft and blimp hangars, commercial warehouses, portable military field structures, and the like. A wide variety of doors are currently used in industrial and other settings. For example, one type of movable door consists of a series of generally horizontal panels disposed one on top of the other with each panel hinged to the panel above. Stemmed rollers are disposed on opposed lateral edges adjacent a bottom and top location of each door panel. Such sectional doors are typically movable between a closed or blocking position and an open or stored position relative to a doorway. For this purpose, guide tracks having a generally “C” shaped cross-section are provided on either side of the doorway for receiving the rollers disposed on the adjacent edges of each of the panels. Each track has a substantially vertical portion disposed adjacent and parallel to the doorway opening, a substantially horizontal portion disposed above and behind the doorway generally perpendicular to the doorway opening, and a connecting curved portion. A track is positioned on either side of the doorway providing a continuous guide track for receiving the stemmed rollers of the adjacent panel sections. In this construction, the door is substantially horizontal when in the open or stored position. Another type of movable door is a vertically storable door which moves in a continuous generally vertical plane between the closed and open (stored) positions along substantially straight and vertical guide tracks disposed from floor level of the door opening to a location above the doorway opening. The lifting force needed to counterbalance

the door is recognized to vary so that different types of lifting assist devices are used to provide a statically balanced overhead door i.e. a door that will maintain a position assigned to it by an operator (user). The position can be closed, open or any location in between.

One type of garage door operating mechanism is the so called torsion spring control system. The torsion spring control system uses a shaft around which are disposed control springs to provide the counterbalance for the door. This type of mechanism avoids the use of extension springs but the torsion spring is exposed and can provide a source of injury if repairs or adjustments are attempted by one not skilled in working with such devices.

Another type of counterbalancing mechanism comprises horizontally extendable springs disposed above and generally parallel to the horizontal portion of the guide tracks for counteracting the effect of gravity on the door as it moves between a closed and an open (stored) position or from an open to a closed position. Such counterbalance devices typically include a cable system with a pair of cables attached to the opposite edges of the door with springs connected to each of the cables. In the door open or stored position the spring is not extended, eg. Relaxed or compressed. When the door moves from the stored position, the spring extends or is streched providing a force which counteracts the weight of the door. In this way, the spring controls the descent of the door as it moves toward the closed position. Conversely, when the door is raised from the (doorway-blocking) closed position, the contracting spring provides a lifting force which makes the door easier to raise. Unfortunately, such mechanisms are complicated to assemble, they lack aesthetic appeal and expose the user to potential injury if the spring or cable breaks.

It would therefore, be desirable to house counterbalancing mechanisms within the door itself, thereby providing a more user friendly installation and an aesthetically pleasing door assembly with internal components that are unexposed reducing the potential of injury to a use