wrench problem

# wrench problem - The two shafts of a speed-reducer unit are...

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The two shafts of a speed-reducer unit are subjected to couples of magnitude M 1 =15lb ft and M 2 =3lb ft respectively. The unit weighs 60lb and its center of gravity is located on the z -axis at z =6in. Replace the weight and the two couples by an equivalent wrench and determine (a) the resultant force, F R , (b) the pitch of the wrench, (c) the point where the axis of the wrench intersects the xz -plane. GIVEN: M 1 =15lb ft FIND: (a) F R M 2 =3lb ft (b) p (pitch) W =60lb (c) point where wrench axis intersects Z =6in=1/2 ft 12 1 2 The only force acting is the weight. ˆˆ 60 ˆ () 6 0 Take moments about the origin (o) ˆ 1 0 0 ( 30) 2 06 0 0 45 3 (moment vector divided into c a t =− = =++ =+ R R o oo o Fj j F ij k Mi j i j MM M Wl b lb M M lb f omponents parallel and perpendicular to ) ˆ 60 (45 3 ) 3 60 We want to displace the line of action of to cancel out the component . where is the vecto o R t  =• = + =   R R o Ro oR F F j j FM Mr F r Ml b f F r from the axis of the wrench to the point that the moments were taken about originally (in this case, the origin).

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## This note was uploaded on 04/12/2009 for the course MEM 202 taught by Professor Cook during the Winter '08 term at Drexel.

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wrench problem - The two shafts of a speed-reducer unit are...

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