Scissor Jack Design for Car Repair Shop

W↓
A/\B
C\/D

In this very crude diagram, W is the weight of one corner of the car, ABCD is the rhombus formed by the compression parts of the jack, and the horizontal line E (I couldn't fit the E into the picture) is the screw.

If θ is the angle between A and E, and F the tensile force exerted by the screw, then
F = W/(2 tanθ). [I think, but it is late here so I am getting sleepy.]

However, W varies from zero as the lift is started to potentially as much as about 1/2 the weight of the whole car. For what seems like a simple device, this is actually a worthy and challenging exercise.

Nice link.

didn't get a chance to review it, wish I had this about 10 years ago when I did one.

The thread can be a piece to check against crack generation it depends on the type of thread you intend to use and on the filet at thread root. A metric thread will be more sensitive than other types.

Consider as well the possible defects coming from turning on the lathe with a higher roughness they can really be dangerous. If you come to high risk give as solution a roller burnishing at the filet it generates a compressive residual strain which reduces a lot the risk of crack generation. This will bring you a better mark.

You have to consider cracking and crack propagation, and premature wear from safety considerations.

Hot rolled threads are smoother, without starter cracks compared to a cut one.

Aircraft grade is the highest grade generally, reasonably available.

But, my vote goes for the trapezoidal thread used in lathes automatic feed. It has very smooth ground surface, giving a large bearing area. The bronze (split) nut has to be at least 10 turns long for good load distribution. Lubrication is regularly required. Even if it turns out too expensive, this would be my reference, the cleanest design.

If, and when cheaper components are desired, you at least have good design to derate the new components from. Most likely, massively. The male thread will have to be smooth and hard. The nut softer, like bronze. Otherwise galling will destroy them in a short order. A failing bolt/nut means a falling car!!!