The spring-held follower A B has a mass of 0.5 kg and moves back and forth as its end rolls on t

step 1 Hi everyone. So what we have is, again, a spring held follower that has a mass of 0 .5 kilograms

The spring-held follower A B has a mass of 0.5 kg and moves...

The spring-held follower $A B$ has a mass of $0.5 \mathrm{kg}$ and moves back and forth as its end rolls on the contoured surface of the cam, where $r=0.15 \mathrm{m}$ and $z=(0.02 \cos 2 \theta) \mathrm{m}$ If the cam is rotating at a constant rate of $30 \mathrm{rad} / \mathrm{s}$ determine the maximum and minimum force components $F_{z}$ the follower exerts on the cam if the spring is uncompressed when $\theta=90^{\circ}$.

Key Concepts

Cam-Follower Mechanism

This concept deals with systems where a cam with a specially designed profile converts rotary motion into a prescribed follower motion. The geometry of the cam, defined by functions like r(?) or other profiles, directly influences the path and dynamics of the follower, and consequently the forces that are transmitted between the cam and the follower mechanism.

Angular Kinematics

Angular kinematics involves studying the motion of bodies in rotation. With a given constant angular velocity, the angular displacement, velocity, and acceleration play a key role in linking the rotational movement of the cam to the linear or curvilinear motion of the follower through time-dependent relationships and chain rule differentiation.

Differentiation in Kinematics

When the follower motion is defined by a mathematical function of the cam angle, differentiating that function with respect to time using the chain rule allows one to determine velocities and accelerations. These time derivatives are essential for analyzing the dynamic behavior of the follower and for calculating inertial forces acting on it.

Newton’s Second Law in Dynamics

Newton’s second law states that the net force acting on an object is equal to the mass of the object times its acceleration. In cam-follower systems, once the acceleration of the follower is obtained (through differentiation), this law is applied to compute the dynamic forces, such as the inertial component acting on the follower, which is critical for understanding the load transmitted through the mechanism.

Spring Mechanics

Spring mechanics involves understanding how springs store and release energy. The force exerted by a spring is typically proportional to its displacement from the equilibrium (uncompressed or unstretched) position. In many cam-follower systems, including the one described, the relationship between the spring’s compression and the force it exerts on the components is essential in determining the effective force components acting on the cam.

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