I. Background Theory:

Solenoid valves, which are electromagnets with movable cores, can serve as useful mechanical actuators. They are relatively inexpensive, simple in design, easy to make, fast in their response to input current, and capable of delivering a strong force relative to their size. These features would make solenoid actuators preferable to conventional electromechanical linear actuators or linear motors in motorized applications. Mechanical tendons actuated by solenoids can offer several advantages over conventional robotic drive systems including lower cost, faster speed, better accuracy, and negligible friction. These advantages can especially be pertinent in the handling and manufacturing of tiny, lightweight goods or goods that can't be held or touched. A common machine that uses linear actuators is your typical computer printer.

Unfortunately, a lone solenoid can't function as a linear actuator without an opposing force. If a magnetic object was placed in a magnetic field with stored potential energy, the object could not be stabilized in a stationary position. The field would have no minima of potential that could serve as an equilibrium position. Let's say that there were two permanent magnets secured to some sort of non-magnetic base (such as an aluminum plate) so that they would face one another. Now, let's say an iron marble was perfectly positioned equidistantly between the two magnets so that the net force on the marble would be zero, rendering it stationary.

Let's say that some outside force were to nudge this iron marble to the left. The iron ball would not go back to its original position. Instead, it will keep rolling to the left until it hits the left magnet. This is because the pulling force exerted by the left magnet on the ball would become stronger while that exerted by the right magnet would become weaker.

In control systems theory, a position or state is described as stable if the system will return to it without any outside influence. The equilibrium position of the iron ball would be described as unstable because if another outside force were to slightly push it out towards one of the magnets, it would move away from the equilibrium position, not towards it. [1]

Thus, a solenoid can't passively stabilize its plunger at an arbitrary displacement, which is a requirement for any viable actuator. Magnetic actuators can initiate movement of a workpiece but not control the direction and magnitude of the movement. In order to move a payload to a desired position using magnetic actuators, it is necessary to utilize multiple solenoids and constantly vary the force they exert using active feedback control. The payload must always remain in tension while being moved.

Now, let's say that the two permanent magnets are replaced by two solenoids. The amount of current that flows in the wires wound around each solenoid can be controlled by a microprocessor. Remember, the magnetic force exerted by a solenoid is proportional to the amount of current that flows through the wire. Let's also say we are able to sense the position or displacement of the ball. If the ball is now nudged to the left, the controller will sense this and automatically decrease the current in the left solenoid while increasing the current in the right solenoid. This will cause the magnetic pulling force exerted by left magnet to weaken and the force exerted by the right magnet to strengthen. This will bring the ball back to the center.

[1] S. Earnshaw, "On the Nature of the Molecular Forces which regulate the Constitution of the Luminiferous Ether," Transactions of the Cambridge Philosophical Society, vol. 7, pp. 97-112, 1942.