Urban Maths: The Garage Door Equation

摘要

Not that I'm particularly clumsy or anything, but I pushed a little too hard on the garage door this morn- ing and managed to get it stuck part way open! It is an overhead swing door, so I had to crawl under the bottom to get inside the garage in order to examine the support mechanism - which I've never stopped to think about, nor even noticed, before - to see what needed to be done to fix it. It turns out that there is quite a simple support structure (see Figure 1 for an illustration of a section through one side). On each side (width-wise) of the door is a rigid pivot arm con- nected to the top of a support pillar on the garage wall, and to the garage door part way down. Though these connections are fixed in place they both allow rotation about the fixture point. Fixed lower on the door is a bearing that also allows the door to rotate, but runs in a channel connected to the support pillar so that that part of the door is constrained to move vertically up and down only (I had managed to push the bearing out of the constraining channel on one side of the door).