Figure 7.1.4a shows a cylinder and piston connected to a load mass m, which slides on a frictionless surface. Part (b) of the figure shows the piston rod connected to a rack-and-pinion gear. The pressures p1and p2are applied to each side of the piston by two pumps. Assume the piston rod diameter is small compared to the piston area, so the effective piston area A is the same on both sides of the piston. Assume also that the piston and rod mass have been lumped into m and that any friction is negligible. (a) Develop a model of the motion of the displacement x of the mass in part (a) of the figure, assuming that p1and p2are given functions of time. Also, obtain the expression for the mass flow rate that must be delivered or absorbed by the two pumps. (b) Develop a model of the displacement x in part (b) of the figure. The inertia of the pinion and the load connected to the pinion is I.
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