I knew that John Logie Baird invented the lens-type scanning disc, as shown in British Patent GB230,576, filed on 29 December 1923. This sort of lens disc requires a separate lens for each scanning line. Although it is most efficient because it may concentrate all of the light that each lens gathers from the modulated light source into the viewed image, it can be bulkly, difficult to adjust and have balance problems if the lenses have the ordinary single spiral arrangement.
I just realised that another early patent by Mr. Baird, GB265,640, filed 6 August 1925, describes a means to greatly simplify a lens disc scanning system so that far few lenses need be used and they may be arranged in a simple circle rather than a spiral. In this patent, amongst other things, Mr. Baird suggests using one lens disc with a few lenses arranged about a circle for vertical scanning and another disc with a few more lenses arranged about a circle for horizontal scanning, with the discs mounted in tandem. Thus, one disc might have eight lenses for shifting the light from a modulated light source vertically at the line rate and another with eight lenses for shifting the light horizontally at the frame rate.
Thus, in the case of the 32 line system, the vertical scanning disc would rotate at 3000 rpm whilst the horizontal scanning disc would rotate at a leisurely 93.75 rpm. There is no need for a spiral arrangement of the lenses, since they individually displace the image in their respective planes. Even fewer than eight lenses per disc would be possible. I only suggest eight lenses because the fewer the number of lenses per disc the greater the arc through which each lens scans, leading to a greater degree of keystone distortion in the reproduced image.
This would be an interesting configuration to implement. Mr. Baird also suggest substituting a polyhedral mirror for one of the lens discs. I have posted this patent at http://www.taswegian.com/NBTV/images/GB265640A.pdf for reference.