Slider crank mechanism mass moment of inertia

[blaster]

I need help solving a mass moment of inertia for a slider crank mechanism. I've done my best to sketch it in the attachment. This will be used for sizing of a motor.

Homework Statement

Link A has mass Ma and is located Acg distance from its pivot point Z
Link B has mass Mb and is located Bcg distance from its connection to Link A
Block C has mass Mc and has a frictionless retainment vertical of point Z
Link A is at and Angle theta from vertical.
Find the mass moment of inertia about point Z.

Homework Equations

Its been too long

The Attempt at a Solution

Tried using engineering programs to figure it out numerically.

 

[RTW69]

You have three masses, I_tot=m1*r1^2+m2*r2^2+m3*r3^2 where the radius is the distance from z

 

[blaster]

But I want the moment of inertia about z. So the constraints in motion play a part. for example when theta is zero the block mass is not moving much with respect to theta. At 90 degrees the block is moving a lot with respect to theta.

I may have not been clear but the inertia is changing dependent upon theta.

 

[RTW69]

Are you trying to find I_total as a function of theta? If so you can use the law of sines to find the interior angles of the linkage and the vertical distance from block c to z. You need everything in terms of B_tl, theta and A_tl. The distance from B_cg to z can be found using the law of cosines since you found the angle between link B and A using the law of Sines above. Now that you know the distances from the center of mass of each element you can find I_total in terms of theta.

 

[DeeNos]

I would approach this problem by first understanding the concept of mass moment of inertia. Mass moment of inertia is a measure of an object's resistance to rotational motion. It is calculated by multiplying the mass of each particle in the object by the square of its distance from the axis of rotation, and then summing these values for all particles in the object.

In this case, the slider crank mechanism can be thought of as a system of interconnected particles (links A and B, and block C) rotating about point Z. To find the mass moment of inertia of this system, we need to first determine the mass and distance of each particle from point Z.

To do this, we can break down the mechanism into smaller components and calculate their individual mass moments of inertia. For example, we can calculate the mass moment of inertia of link A about point Z using the formula I = Ma * Acg^2, where Ma is the mass of link A and Acg is the distance of its center of gravity from point Z.

Similarly, we can calculate the mass moment of inertia of link B about point Z using the formula I = Mb * Bcg^2, where Mb is the mass of link B and Bcg is the distance of its center of gravity from point Z.

For block C, since it is retained vertically at point Z, its mass moment of inertia about point Z will be zero.

Once we have calculated the individual mass moments of inertia for each component, we can add them together to get the total mass moment of inertia of the slider crank mechanism about point Z.

In summary, to solve for the mass moment of inertia for a slider crank mechanism, we need to break down the system into smaller components, calculate their individual mass moments of inertia, and then sum them together to get the total mass moment of inertia. This information can then be used for sizing of a motor.