Moment of inertia for a system

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To find the moment of inertia for a four-bar linkage and a gear system with three reducers, consulting a theory of machines textbook is recommended. The kinetic energy of the system can be expressed as T = (1/2) qdot^2 I(q), where I(q) represents the generalized inertia dependent on the generalized coordinate q. This approach allows for the extraction of the function I(q) from the kinetic energy expression. It is important to note that the moment of inertia for the four-bar linkage will vary based on the configuration described by q. Understanding these principles is crucial for analyzing the dynamics of mechanical systems.
vikramvv
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1.How to find the moment of inertia of linkage (four bar mechanism), Gear system(having 3 reducers).
 
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consult a book, preferably theory of machines.
 
Calculate the kinetic energy of the system and factor out the generalized velocity so that you have a form that looks like

T = (1/2) qdot^2 I(q)

where I(q) is the generalized inertia which is a function of the generalized coordinate q that describes the system configuration. Then it is a simple matter to extract the function I(q) from this expression. Note that for the four bar linkage it will be variable, depending on q.
 
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