# Slider crank mechanism mass moment of inertia

• blaster
In summary, the problem involves finding the mass moment of inertia about point Z for a slider crank mechanism consisting of three links and a block with frictionless retention. The inertia is dependent on the angle theta and can be calculated using the law of sines and cosines to find the distances from the center of mass of each element.
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.

#### Attachments

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

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.

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.

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.

## What is a slider crank mechanism mass moment of inertia?

A slider crank mechanism is a mechanical system that converts rotational motion into linear motion. The mass moment of inertia is a measure of an object's resistance to changes in its rotational motion. In the case of a slider crank mechanism, it refers to the distribution of weight around the axis of rotation.

## How is the mass moment of inertia calculated for a slider crank mechanism?

The mass moment of inertia for a slider crank mechanism is calculated by summing the individual moments of inertia for each component of the mechanism. This can be done using the parallel axis theorem, which takes into account the distance of each component from the axis of rotation.

## Why is the mass moment of inertia important in a slider crank mechanism?

The mass moment of inertia is important in a slider crank mechanism because it affects the system's ability to accelerate and decelerate. A higher mass moment of inertia means that more force is required to change the system's rotational motion, making it less efficient.

## What factors can affect the mass moment of inertia in a slider crank mechanism?

The mass distribution of the components, the size and shape of the components, and the distance of the components from the axis of rotation can all affect the mass moment of inertia in a slider crank mechanism. Additionally, adding or removing components can also change the mass moment of inertia.

## How can the mass moment of inertia be optimized in a slider crank mechanism?

To optimize the mass moment of inertia in a slider crank mechanism, the distribution of mass needs to be carefully considered. Reducing the mass of heavier components and placing them closer to the axis of rotation can help to decrease the overall mass moment of inertia, making the system more efficient.

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