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<< Click to Display Table of Contents >> Navigation: General Design Information > Cam-Mechanism Design > Dynamics of Cam Mechanical Systems > Gearing Effects |
Often there is some form of gearing in the transmissions, input or output, of a cam system.
We have looked at the effects of gearing on the Transmission Elasticity and Backlash. Loading is affected in a similar way.
The value of force or torque at one side of a gear-pair is converted to a different value at the other side in direct proportion to the velocity ratio of the gears, and the value of inertia is converted in proportion to the square of the velocity ratio.
All the components of a system can therefore have equivalent values of load and inertia referred to the cam for input components or the follower for output components.
The equivalent values are additive, so that a single value can be used to represent all of the components, and the system will behave as if there were no gearing in the transmissions.
The loading and power equations are valid for gearing provided that:
- the sum of all equivalent forces referred to the Follower output - the sum of all equivalent masses referred to the Follower output - the sum of all equivalent torques referred to the Follower output - the sum of all equivalent mass moment of inertia referred to the Follower output - the sum of all equivalent mass moment of inertia referred to the Cam input |
The concept is based on the Power at the output is equal to the Power at the input times the efficiency.
or
Similarly
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The concept of equivalent mass or inertia is based on the fact that at any instant the kinetic-energy of the equivalent mass must be the same as the kinetic-energy of the actual mass.
or
Similarly:
= linear velocity = angular velocity subscripts 1 and 2 refer to the input and output sides of the gear-pair respectively. The gear ratio is obviously:
In the context of a linear motion, a lever is considered as a Gear-Pair. Often, the output transmission consist of a mixture of translating (linear motion) components and oscillating (angular motion) components. The principle of equating power and kinetic-energy still apply.
It depends on whether the linear motion is the output and the rotary motion is the input, or vice versa.
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