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### Force-Torque-Power-Energy Analysis

Overview of Using Basic Force-Torque-Power-Energy Analysis in Machine Design

To create a machine element that moves you will need to provide an energy source that will apply a force or torque on the object. The energy source could be a motor, pneumatic piston, preloaded spring, or gravity. Examples of using an energy in a machine include raising a mass, accelerating a mass, or overcoming friction. Criteria to consider are:
• Energy (Joules). If you do not have enough energy to accomplish a desired task, then there is no way your device will be successful. Accordingly, one of the first feasibility analysis to perform is to calculate your energy needs and availability.

• Power (Watts). Power is the rate at which energy is applied to a system (Watts = Joules/Second). Typically one cares about the speed at which an element operates, so it is necessary to perform a power analysis in addition to energy analysis. Motors and springs have a maximum amount of power that they can provide, which can be used to determine how fast mechanical work can be done. However, if necessary one can increase power by storing energy and then releasing it quickly. Examples include:
• Putting kinetic energy into a rotating flywheel, then having the flywheel release the energy quickly though impact.
• Slowly retracting a spring and then allowing it to release quickly.

• Force and Torque. To initiate motion and continue motion through a desired trajectory, it is necessary that sufficient force and/or torque be provided. A Free Body Diagram analysis must be performed to identify the force and torque needs of your design. It is possible to increase force and torque at the expense of speed using mechanical advantage:
• Levers
• Gears
• Pulleys

• Work is Energy Transfer

Mechanical Work, W, is a transfer of energy. Mechanical energy can be transferred by applying a force or torque over a distance of motion. If there are no energy losses in the system then the chance of energy δΕ=W

• For translation:

W = Distance over which force is applied X Force in direction of motion (units of Nm)

• For rotations:

W = Torque x  radians of rotation (units of Nm)

Necessary vs. Sufficient Conditions

Due to the law on conservation of energy, it is necessary that your energy sources have at least the amount of energy needed by your machine. However, energy alone is not sufficient. If your energy can only be released very slowly, you may not have enough power to get the motion done within the desired time. Finally, motion can only occur if the sum of the force and torques on the object are sufficient. Accordingly, the following applies:
• Energy analysis identifies a necessary condition, but this is not sufficient to ensure that your part will move within the desired time frame.

• Power analysis identifies a necessary condition that takes into consideration the time frame of motion, but it is not sufficient that the part will indeed move since force and torque also needs to be considered.

• Force and Torque analysis will allow one to determine if motion of a part will occur; if the sum of forces on a part is greater than zero then it will accelerate. In this sense Force and torque analysis is a necessary and sufficient condition needed to create part motion. But note, that force and torque analysis at a single instance will not determine the overall time frame that the motion will occur. Note, there is no law of conservation for forces and torques, indeed level and gears can increase the force and torque output, but at the expense of speed output.
The typical analysis for a new machine goes like:
1. Energy analysis to confirm there is enough energy to get the job done.
2. Power analysis to determine if it is feasible to get the motion done within a desired time frame.
3. Force and Torque analysis to determine the proper mechanical advantage and gear ratios needed.
In all cases a Factor of Safety is needed in the analysis to account for items such as frictional losses, non-optimal energy transfer, and other unknowns.

### Measuring Energy Source Characteristics

Before building a machine you will want to quantify how much energy, power, force, and torque you need and compare these to the energy sources you have available. The methods below will show how this can be done for various energy sources.
A good designer will know the amounts of energy, power, force, and torque, from the various sources he or she has. These are summarized in the Team Force-Torque-Power-Energy Analysis which is part of Lab 5.

### Feasibility Analysis Using Force-Torque-Power-Energy Values

See following examples for determining feasibility of preliminary designs.

Seesaw Force and Velocity Example

Raising a Hammer

Shooting/Throwing Projectile example

Cart moving example

Rotating Robot Arm Example

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Nate Delson,
Apr 24, 2018, 6:25 PM