Solved: Prove that the lead l must be less than 2prms for

Chapter 8, Problem 8-73

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QUESTION:

Prove that the lead l must be less than 2\(\pi\)r\(\mu_{\mathrm{s}}\) for the jack screw shown in Fig. 8–15 to be “self-locking.”

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QUESTION:

Prove that the lead l must be less than 2\(\pi\)r\(\mu_{\mathrm{s}}\) for the jack screw shown in Fig. 8–15 to be “self-locking.”

ANSWER:

Step 1 of 6

For the screw to be self-locking, it means that it is in equilibrium even if there is no force applied to its handle.To check this, we'll draw the free-body diagram of the screw.

Note that  is angle which thread makes with the -axis, and the expression for it is:

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