In Exercise 9, what would the distance across the top of the worm thread have to be to make d equal to 0 inches?

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1 Answer
P dilip_k
Jan 25, 2018

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When #d=0# inches the situation will be represented by the modified figure as shown above. The distance across the top of the worm thread then will be #PR#

Now #PR =2PQ= (2PQ)/(OQ)xxOQ#

#=>PR = (2PQ)/(OQ)xx(QC+CQ)#

#=>PR = (2PQ)/(OQ)xx(QC+(CQ)/(CN)xxCN)#

#=>PR = (2PQ)/(OQ)xx(CN+(CQ)/(CN)xxCN)#

#=>PR = (2PQ)/(OQ)xxCN(1+(CQ)/(CN))#

#=>PR = 2tanthetaxx0.75(1+csctheta)#

#=>PR = 1.5(tantheta+tanthetaxxcsctheta)#

#=>PR = 1.5(tantheta+sectheta)#

#=>PR = 1.5(tan15^@+sec15^@)~~1.95# inch

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