The Iron Arms TM rotating forearm grips exercises the forearms by resisting
rotation of the handle grips inward and outward-see Figure P12.32 and Figures
P2.2 and P2.3 (Chapter 2 ). The rotation of the gripped handle, about its
center, is opposed by the force on the free end of the spring. The handle
assembly is shaped like a "D." The curved portion of the D slides smoothly
inside the hollow ring; the straight portion of the \(D\) is for hand gripping.
The handle grip length is approximately \(4.0\) in. long and \(1.25\) in. in
diameter. The rings have an outer diameter of \(7.75\) inches and an inner
diameter of \(5.375\) in. The entire Iron Arms assembly has an overall length of
\(15.40\) in., a width of \(7.75\) in. (outer ring diameter), and a thickness of
\(1.25\) in. Each spring has squared ends with 29 total coils and is made of
carbon steel wire. The mean coil diameter is \(.812\) in., and the wire
diameter, \(d=0.088\) in. The coil outer diameter is \(0.90\) in. The spring has a
free length of \(10.312\) in., and a compressed length of \(9.75\) in. when
assembled and in the "starting position."
(a) Calculate the energy stored in each helical spring after the spring is
rotated \(90^{\circ}\) from the starting position.
(b) Calculate the initial force on the fore-end of the spring to start
rotation of one handle and the force on the free end of the spring when the
handle has rotated \(90^{\circ}\).
(c) Calculate the spring constant, \(k\), for the spring.
(d) Determine (i) the height of the spring when compressed solid, (ii) the
corresponding force on the free end of the spring, and (iii) the rotation of
the handle in degrees from the handle start position.
(e) Select a carbon steel coil spring material and determine if the spring is
designed for infinite life.
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