Concept explainers
The test rig shown was developed to perform fatigue testing on fitness trampolines. A motor drives the 200-mm radius flywheel AB, which is pinned at its center point A, in a counterclockwise direction with a constant angular velocity of 120 rpm. The flywheel is attached to slider CD by the 400-mm connecting rod BC. The mass of the connecting rod BC is 5 kg, and the mass of the link CD and foot is 2 kg. At the instant when θ = 0° and the foot is just above the trampoline, determine the force exerted by pin C on rod BC.
Fig. P16.127
Find the force exerted by pin C on rod BC for fitness trampoline.
Answer to Problem 16.127P
The force exerted by pin C on rod BC is
Explanation of Solution
Given information:
The radius of the flywheel AB is
The mass of the connecting rod BC is
The mass of the link CD and foot is
The length of the rod BC is
The angular velocity is
The angle is
Calculation:
Convert the unit of angular velocity from
Consider the acceleration due to gravity as
Calculate the weight
Calculate the weight of rod BC
Substitute
Calculate the weight of link CD
Substitute
Sketch the geometry of the rig as shown in Figure 1.
Refer to Figure 1.
Calculate the angle
Calculate the position vectors
Position of B with respect to A.
Position of C with respect to B.
Position of G with respect to B.
Calculate the moment of inertia
Substitute
Sketch the Free Body Diagram of the rod CD as shown in Figure 2.
Refer to Figure 2.
Apply the Equilibrium of forces along y direction as shown below.
Substitute
Sketch the Free Body Diagram of rod BC as shown in Figure 3.
Refer to Figure 3.
Apply the Equilibrium of forces along x direction as shown below.
Substitute
Apply the Equilibrium of forces along y direction as shown below.
Substitute
Apply the Equilibrium of moment about G as shown below.
Substitute
Calculate the velocity
Substitute
Calculate the velocity
Substitute
Resolving the i and j components as shown below.
For i component.
For j component.
Substitute
Calculate the relative acceleration
Substitute
Calculate the relative acceleration
Substitute
Resolving i and j components as shown below.
For i component,
For j component,
Substitute
Calculate the relative acceleration
Substitute
Resolving i and j components as shown below.
Calculate the reaction
Substitute
Calculate the reaction
Substitute
Calculate the reaction
Substitute
Substitute
Calculate the reaction at C as shown below.
Substitute
Therefore, the force exerted by pin C on rod BC is
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