Both Beacon Hill worms in their profiled 'housings' are shown alongside with the larger, 34t timing pulleys fitted. Note how the worm size and pitch have to match its own particular wormwheel. The 11" wheel worm is in the foreground with the 8" wheel worm behind.
The number of teeth  remains constant. While the circumference of the wormwheel sets the tooth [or screw] pitch. Only specific wheel diameters/circumferences will produce teeth of a useful pitch which can be actually be cut as a "screw thread" for the matching worm.
A worm is rather like a section of screw thread whose diameter must also match the required pitch of its wormwheel. A completely random choice of [odd] pitch would make the worm all but impossible to produce in a normal screw-cutting lathe. A worm is not a normal [i.e. nuts and bolts] screw thread. Because the tops and bottoms are flattened in the form of an ACME thread. These threads are commonly used for vices, G-cramps [C-clamps] and other very heavily loaded screwed devices.
Only the flanks [sides] of the teeth do the driving and the worm must not bottom in the wheel teeth. The two components must have just enough clearance to avoid backlash. Without any free rotary movement of the wormwheel.
The worm brackets must also be firmly fixed with suitably large bolts. Or the drive power available will dislodge the worm housings. Meanwhile the worm housings need fine, radial screw adjustment towards and away from the circumference of the wormwheels. There is really only one ideal position for a worm nestled against its matching wormwheel. It must be square to the wheel or the threads and teeth will not allow the necessarily fine adjustment needed.
The pulley to worm shaft fixing screws must lodge onto small flats or dimples on the worm shaft to avoid them loosening over time. The tiny grub screws provided might be better replaced with stainless steel, hex socket head screws. The worm housing bearings can also be prevented from linear movement. The tiny grub screw on top of the bearing housing is hardly adequate. Over-tightening can easily lock the bearing against rotation! An outboard plate at each end of the housing will prevent bearing shift.
Wormwheel and worm mock-up on oak blocks.The arrows show the positions of the radial nylon plugs which provide the slipping clutch. Grubs screws provide the adjustment of pressure.
I originally made 5mm [1/5"] worm support plates but these could still flex. A later find of a long length of scrap, 10mm aluminium [also 6" wide] offered a much stiffer alternative.
The availability of scrap aluminium is not an ideal design parameter for telescope making but one is always incredibly grateful for whatever turns up. One should never try to haggle or the scrap dealer will quickly lose interest in helping the oddball.
I have been extraordinarily lucky in finding enough 10mm and 20mm plate in good condition at a single scrap merchant. Alas, finding suitably heavy alloy angle has resisted all my repeated visits. Metals can be bought on eBay UK and DE but the Danish metal stockholders will not deal with private customers. Trying to buy 4mm plate from a local engineering firm proved very costly after they had guillotined a couple of modest pieces to size. A return visit provided no suitably heavy angle for worm support.
The new 10mm support plates will still be trapped between the bearings housings and the axes heavy flange bearings. The four equally heavy 16mm, [~3/4"] corner studs [all threads] will prevent all movement.
It will be up to me to provide finely adjustable but immovable support for the worm housings. An earlier plan to use solid oak support blocks was ditched when the blocks changed their dimensions with moisture content. They could also be compressed by their fixing bolts. After carefully setting up the fit between worm and wheel by feel alone I would come back and find the friction or backlash had changed. Not a good start.
So the supporting material must be made entirely of metal and of adequate cross section to avoid all flexure. The problem is that there is quite a space to make up between the 10mm support plates and the bases of the worm housings. As can be seen by the height of the oak blocks. More on this later.