THE POWER TAKE-OFF KITS:

The accessory "Handyman Kits" were the single feature of the Singers that made them so unusual.
To my knowledge, the only other manufacturer that offered a power take-off on a rotary was Condeco's Austral-Villiers
Adaptomatic rotary; but with no developed accessories.

The Singer offered specific kits for differing applications:-
Kit number 1 - house and garden pump
Kit number 2 - compressor for spray painting
Kit number 3 - garden & house spray [see 'For The Record' below]

Here are a couple of photographs of the attachments.
The photos are courtesy of the State Library of New South Wales.
Their record indicates that the accessories were made for Singer by CIG Arnold DeVilbiss Tuffy.
The photos were taken in late 1964 at the Singer factory at Riverwood:-

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Photo Credit: http://trove.nla.gov.au/work/12251058?q=singer+mower&c=picture

The PTO arrangement appears to have been via an engine crankshaft pulley and belt to a coupling at the rear.
The advertising suggests that both side and rear discharge mowers could accept the accessory kits.
Here is an illustration of the PTO coupling:-

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TO BE CONTINUED ...