A clipboard that is used for holding and writing on paper is hown. The clamp ABC

Question

A clipboard that is used for holding and writing on paper is hown. The clamp ABC has a torsional spring at pin C with stiffness kt=2in*lb/rad. To release the clamp so that the paper may be inserted/removed, the user applies a vertical force P. Determine the pretwist of the torsional spring (in terms of # of turns) so that the clamp provides a clamping force of 6lb at point A when P=0, and determine the force P needed to release the clamp. Assume the contact at A is frictionless.

Thank you in advance.

A clipboard that is used for holding and writing on paper is hown. The clamp ABC has a torsional spring at pin C with stiffness kt=2in*lb/rad. To release the clamp so that the paper may be inserted/removed, the user applies a vertical force P. Determine the pretwist of the torsional spring (in terms of # of turns) so that the clamp provides a clamping force of 6lb at point A when P=0, and determine the force P needed to release the clamp. Assume the contact at A is frictionless.

Explanation / Answer

To find theta, set the value given for A, multiplied by the moment arm from A to C, equal to theta multiplied by the value given for k. Looks like:

F(a)(Mac)=(theta)(k)

For this problem,

6(2.1)=theta(2) -----> theta = 12.6/2 ----> theta = 6.3

This number is in radians. You need this is "number of turns" and the conversion from radians to turns is .159154943.

So 6.3*.159154943 = 1.00268 turns

Then, for P, you set P * Moment arm from C to P = force at A * moment arm from A to C

(P)(Mcp)=(A)(Mac)

P(.8)=(6)(2.1)

P = 15.75 lbs

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