If a pogo stick was to be reinvented and you were to choose the spring type. What type of spring will generate the most return of kinetic energy compared to least amount of force needed to compress the spring...you can use leaf, coil, scissor, compression, or extension type spring as the linkage factor is irrelevant to this question... i assume a cam can be involved as archers use a 50lb of pull to generate 275fps arrow velocity...if i use your answer for my manufacturing dilema, you will be paid hansomly.. PS i am not building a pogo stick

To generate (or store) a large required amount of energy with a low compression force, you obviously need a low value of the spring constant, k.

Energy = (1/2)k X^2
Force = k X

Energy/Force = (1/2) X
= (1/2)*sqrt(2E/k)

That is the reason coil-type springs are used. They have low sprng constants in spite of the high elastic modulus (stiffness) of the metal materials used to make them.

Compressed air (like the air pockets in some running and basketball shoes) can also be a beneficial design approach.

When selecting a spring type that would generate the most return of kinetic energy with the least amount of force needed to compress the spring, the key factors to consider are spring constant (k), which represents the stiffness of the spring, and the energy stored in the spring (E).

Among the options you provided (leaf, coil, scissor, compression, and extension spring), the coil spring is typically the most efficient option for maximizing energy return while minimizing force required to compress it.

Here's how you can arrive at this conclusion:

1. Understand the basics: To analyze the performance of various spring types, it's important to consider Hooke's Law, which states that the force required to compress or extend a spring is directly proportional to the displacement (distance) it undergoes. The equation is F = kx, where F is the force, k is the spring constant, and x is the displacement.

2. Assess spring constant: Comparing the spring constants of different types of springs, the coil spring often provides a high spring constant, meaning it is relatively stiff and requires less displacement (compression) to generate a specific force. This implies that you would need to apply less force to compress a coil spring compared to other types.

3. Evaluate energy storage: Another crucial aspect is the energy stored in the spring. The energy stored in a compressed or extended spring is given by the equation E = (1/2)kx², where E is the energy and x is the displacement. The coil spring can store a significant amount of energy for a given compression due to its high spring constant. This translates into a more efficient transfer of kinetic energy when the spring is allowed to decompress.

4. Consider cam involvement: If a cam is involved in the design, it can leverage the mechanical advantage of the coil spring by providing a gradual increase in force during compression. This would allow you to maximize the energy stored in the spring for a given amount of force applied.

Based on these considerations, the coil spring is likely the most suitable choice for generating the most return of kinetic energy while requiring the least amount of force to compress. However, it's important to note that the specific design of the pogo stick and the desired performance characteristics can also impact the final choice.

Remember, consulting with mechanical engineers or experts in the field can provide further insights and help you make informed decisions for your manufacturing project.