That is a good question and by coincidence I just measured my 2 Kenmore machines yesterday. They are both cabinet models and both different so these measurements will let you know if certain Kenmore cabinets are even an option.
The bed size of my 117.841 is 17 x 7 3/8. That machine has square corners so the cabinet does too.
The bed size of my 117.740 is 15 x 7. That machine has rounded corners so the cabinet does too.
I'd recommend that you measure your machine and take a tape measure with you when you are cabinet shopping.
Can you post the measurements of your Singer? I'd be curious what they are. I only have my Kenmores.