Trapezoidal thread gauge are screw thread profiles which have trapezoidal outlines. They offer ease and high strength of manufacture. The vice where large loads are required, as in a vice or the lead screw of a lathe. Their standardized variations include self-centering threads, multiple-start threads, and left-hand threads (which are less likely to bind under lateral forces). Trapezoidal thread forms 

The real trapezoidal thread gauge and still probably the one most famously encountered worldwide, is the Acme thread form. It is quite easier to cut via either single-point threading or die than the square thread is because the latter’s shape needs tool bit or die tooth geometry that is poorly suited to cutting; it wears better than square because the wear can be compensated for; it is, and then a sized square thread, and it makes for smoother engagement of the remaining nuts on a lathe lead screw than square does.

The Trapezoidal thread gauge is similar to the Acme thread form, except the thread angle is 30°. It is arranged into a code by DIN 103. However, metric screw threads are generally more dominant worldwide than imperial threads, the Acme thread is quite popular worldwide, and they may have than the trapezoidal metric thread. This is not shocking, as manufacturers today are capable of making whichever threads are best and good for any given application based on customer expectations or tooling availability. Probably, it may be that the tooling for Acme threads has been so dominant (compared to trapezoidal metric). Customers want Acme threads for power screws irrespective of metric standards used elsewhere in the product. Whitworth Thread form 

Whitworth Thread gauge

The Whitworth Thread gauge was the world’s first national screw thread standard,[1] devised and specified by Joseph Whitworth in 1841. Until then, the only standardization was what little had been carried out by people, individuals and companies, alongside with some companies’ in-house standards spreading a bit within their industries. Whitworth’s new standard specified a 55° thread angle and a thread depth of 0.640327p and a radius of 0.137329p, whereby p is the pitch. The thread pitch increases with diameter in steps shown and stated on a chart.

The Whitworth Thread gauge is based on a fundamental triangle with an angle of 55° at each peak and valley. The sides are at a flank angle of Θ = 27.5° perpendicular to the axis. Thus, if the thread pitch is p, the height of the fundamental triangle is H = p/(2 tan Θ) = 0.96049106 p. However, the top and bottom 1⁄6 of each of these triangles are cut off, so the actual depth of thread (the difference between major and minor diameters) is 2⁄3 of that value, or h = p/ (3 tan Θ) = 0.64032738 p. The peaks are further reduced by rounding them with a 2× (90° − Θ) = 180° − 55° = 125° circular arc. This arc has a height of e = H sin Θ/6 = 0.073917569 p (leaving a straight flank depth of h − 2e = 0.49249224 p) and a radius of r = e/ (1 − sin Θ) = 0.13732908 p.