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Can anyone help me to know why do we use screw driver of longer length of the wrench from the centre of the nut held between the jaws to the place on the handle where you pull (or push) on the wrench that is why do not we use screw driver with long handle as per this formula moment of force = F *r . i want to ask something this Torque, τ, equals r × F. Its magnitude is rF sin θ. Here, r is either the radius of the screwdriver handle or the length of the wrench from the center of the nut held between the jaws to the place on the handle where you pull (or push) on the wrench. F is the force you apply, and θ, of course, is the angle between the vectors r and F. For the screwdrivers, since you wrap your hand around the handle and turn the screwdriver, you apply the force at 90° to the radius of the handle. While it is possible to hold the wrenches at various angles, when you wrap your fingers around the wrench handle, the most natural angle at which to hold it is 90°. This, of course, maximizes the torque you can exert, and unless the nut or bolt you are trying to turn is in an awkward location, it is how you would normally apply force to the wrench handle.

As noted above, r is the radius of the screwdriver handle or the length of the wrench handle (from the center of the nut or bolt being turned to where you hold the wrench), so the larger the diameter of the screwdriver handle, or the longer the wrench handle, the greater the torque you can develop by applying a given force.

You can think of screwdrivers and wrenches as modified class one levers (see 20.03, 28.06 or 32.03 -- Lever arm). A class one lever is one in which the “load” and the “effort” are on opposite sides of the fulcrum. Here, the fulcrum is the center of the screw or nut (or whatever you are turning with the screwdriver or wrench) and, hence, the central axis of the screwdriver, assuming it is centered on the screw, or a point between the jaws of the wrench. The radius where the load is applied depends on the particular situation. First of all, if the screwdriver blade fits tightly in the slot of the screw head, the moment about the blade is the integral of all the moments from the center to the edges of the blade. If the fit is not tight, torque is transmitted only at the edges of the blade, so the moment is merely that applied at the edges, and the radius is half the width of the blade. In this case, the mechanical advantage offered by the screwdriver is the ratio of the handle radius to half the blade width (or the handle diameter to the blade width), or rhandle/rblade. The overall actual mechanical advantage, however, can depend on the dimensions of what you are turning with the screwdriver. For example, if the diameter of the screw thread is greater than the width of the screwdriver blade, then the overall mechanical advantage is reduced. If the screw thread is narrower than the blade, however, the mechanical advantage is greater. In either case it becomes rhandle/rthread.

With the wrench, the radius at which the load acts is the inner radius of whatever you are turning with the wrench, for example, the radius of the thread of a nut. If we call the distance from your hand to the center of the nut rhandle, and the radius of the thread of the nut rthread, the mechanical advantage the wrench affords is the ratio rhandle/rthread. Holding the wrench close to the jaws lowers the mechanical advantage, and holding it as close as possible to the far end of the handle maximizes the mechanical advantage. Can any me what does it means.

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  • $\begingroup$ This is really hard to read, it's one long sentence. It is also more of an engineering question IMO. $\endgroup$ – JMac Jul 4 '17 at 11:43
  • $\begingroup$ There is no need to make a screw driver bigger than necessary (you need to be able to carry it) $\endgroup$ – Steeven Jul 4 '17 at 12:01
  • $\begingroup$ It seems to me that OP is confused about what a "screwdriver" is. $\endgroup$ – Hot Licks Mar 30 '18 at 2:07
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Often it's a question of space constraints and the expected torque of a handheld screwdriver.

Screwdrivers are generally a small portable tool for dealing with objects that are fairly easy to service and don't require power machinery. Often times with a screw driver, you are working in tight spaces with limited movement.

Having a large arm could make it very difficult or impossible to get access to an area with a screwdriver. The arm might not fit, or may not be able to do full rotations (you could add a ratcheting system, and there are screwdrivers with ratchets available).

You can find screwdrivers (and more often hex keys) that have wider handles to give more torque. Regular screwdrivers are designed to be more universal, and are often smaller so that they can be used in spaces with limited access if required.

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