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The Steadicam's articulated arm is a lot like a spring-loaded, swing-arm lamp. It consists of two arm segments, connected with a pivoting hinge. Each arm segment is a sort of parallelogram: It's made up of two metal bars, fastened to two metal end blocks. Just as with any parallelogram, the metal bars will remain parallel with each other (or nearly parallel) no matter how the arm is positioned. Since the end blocks are secured to the ends of the parallel bars, they'll remain in the same position as the arm swings up and down (as you can see in the diagram).
If you were to attach a light to one of the end blocks in this design, as in a swing-arm desk lamp, the light would continue to shine in the same direction as you moved the arm up and down. In the same way, a camera attached to one of the end pieces keeps pointing in roughly the same direction. But in order to keep the camera sled absolutely level, the arm grips it with a free-moving gimbal. The sled's own weight distribution keeps the camera balanced (as we'll see later).
In this setup, the weight of the camera sled constantly pulls the arm downward -- it works to bring the parallel metal bars together so that the front block (A and B) of each arm segment is lower than the rear block (C and D).
To counteract this downward force, the parallel metal bars in each arm are connected with a spring system. The spring system works to close the parallelograms the opposite way -- so that the front blocks are higher than the rear blocks. The system is precisely calibrated to exactly match the downward force of the sled's weight. In this way, the arm and the camera sled will stay in the same position until the cameraman shifts the camera up and down.
In the original Steadicam design, the bars were connected directly with springs. In the modern Steadicam, the arrangement is a little more elaborate, but it serves the same function. You can see how this system works in the illustration.
The lower bar in each arm segment is actually a hollow cylinder, with a large coiled spring inside. The spring is attached to a pulley, which is connected to a drum by a pair of metal cables. The drum, in turn, is connected by a cable to the opposite end block. In this configuration, the spring pulls the pulley back, which rotates the drum, which pulls the cable attached to the opposite end block. In this way, the strength of the coiled spring works to move the parallel metal bars opposite the force of the camera's weight.
The advantage of this system is that it's easy to adjust the spring strength to match different weight loads. The cable can be moved up and down on the end block. Moving it up rotates the drum, which pulls the pulley in closer, which stretches out the spring. This increases the pulling force working against the weight force.
The articulated arm essentially acts as a shock absorber for the camera sled. When the operator moves, the base of the arm moves as well. But the spring system in the rest of the arm responds to the weight of the sled. Instead of a sharp jolt, the camera shifts its position smoothly. The arm also frees up the person's hands -- it hangs directly on the vest, so the operator doesn't have to do anything to hold the camera sled up. He or she can concentrate on positioning the camera to get the best shot.