Determine the contact size in square inches per side for the

Determine the contact size in square inches (per side) for the fingers of a parallel gripper to meet the following specifications: rubber coated aluminum contact surfaces with a use (coefficient of static friction) of 0.77, part that is a cardboard box weighing 210 newtons and capable of withstanding a maximum pressure of 1.4 psi, application of a 26 percent lifting safety factor, and a maximum vertical acceleration of the robot arm of 30 centimeters per second squared. (Enter your answer as a number without the units.)

Solution

Ar = contact area per side of the finger =?

Mu = Coefficient of Friction = 0.7, Mass of Cardboard box, M = 210 N = 210/9.8 [kg]

Maximum pressure on the contact area, p = 1.4 psi = 1.4*6895 [Pa]

Lifting safety factor SF = 0.26, Maximum lifting acceleration, a = 30 cm/s² = 0.30 m/s²

Maximum downward force on the gripper (both surfaces) F1 = = M*(g + a)

Force due to gripping pressure - both sides, F2 = 2Ar*p*Mu

Designed capacity of gripping force, F3 = F2*SF

F3 F1

Hence, M*(g + a) = 2*Ar*p*Mu * SF

Hence, Ar = M*(g+a)/(2*p*Mu*SF) = 210/9.8 [kg]*(9.8 + 0.3) [m/s²]/(2*1.4*6895 N/m² * 0.77 * 0.26) = 0.056 [m²]

Hence contact area = 0.056 [m²]*1550 [in²/m²] = 86.8 [in²]