When I originally posted this question 2021-04-08, I was inspired by pulley physics, especially after viewing these videos at this link and this link and this link. It is not necessary to go to these links. Just to bear in mind the concept that inspired my question which is that less kinetic force on one end is needed through a series of simple machinery to lift more weight at the other end. I began to wonder if there is an equivalent method in physics to do something similarly in axial gear machinery so that the force applied on one end of the axle is amplified to move more weight, cause more torque, and increase the rotational speed on the other end of the axle.
I began to conceptualize something along the lines of the above planetary gear set (epicyclic gear train), where input force/energy on one end of the axial is amplified through a series of transmission gears so that the output side has more speed and torque. The machine I envision is a simple compact machine that converts in line axial rotational motion into mechanical advantage so that the same work can be done with less applied force.
The question then becomes this: How can rotational kinetic energy be amplified, and does anything already exist that accomplishes this?
Conceptually, what I am after is the mechanical analog of what the electrical transformer/inverter does when input electrical energy goes into the system. However, in this present question, it is not electrical energy, but kinetic energy that is being transformed/inverted/amplified. So a related physics question would be: how can kinetic energy be amplified in rotational machinery and applied to the simple compact machine described in this present post?
These are my questions which I will be most grateful to know. Any suggestions or insights would be most helpful.