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Bending motion is stereotyped by the action of the hinge (Fig. 8-4). Your elbow bends, and so does your knee. Everything that you build with a hinge has that same bending motion. If you look at the hinge from its edge, you can see that it is actually rotating around its hinge pin. Bending is a specialized form of rotation. If you have two heavy parts that need to bend relative to
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CHAPTER 8 Joints
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Fig. 8-4.
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Hinge.
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each other, you can build a hinge using the bearings or bushings described in the previous section.
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While rotating and bending motions can be used for most of your mechanical needs, sometimes parts need to slide along a straight line. Some of the same tools you used for rotation can be used for sliding (Fig. 8-5). For example, the bushing works just as well for sliding motion as it does for rotation. You can unroll a rotating ball bearing to make a sliding track. You probably have these tracks on the drawers in your kitchen or desk. The cutaway illustration in Fig. 8-5 is just that, an illustration. Actual linear bearings need a way to lock the two tracks together, so the system doesn t just fall apart. The wheels on your car or bike provide a form of sliding motion, if you consider the movement of the car against the road instead of the motion of the wheels relative to the car. Wheels on a track are similar to a ball-bearing raceway. Roller coasters and trains use wheels that lock onto a xed track.
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While sliding and rotating joints cover many motions, there is one more joint to look at, the ball and socket. Your hip and shoulder operate on the ball and socket principle, giving your arms and legs a wide range of motion.
CHAPTER 8 Joints
Fig. 8-5.
Sliding.
Fig. 8-6.
Ball and socket joints.
Rotating and sliding mechanisms provide motion along one axis (unless you allow your slider to rotate around its shaft). They are said to have one degree of freedom; they are free to move along one dimension. The ball and socket has two degrees of freedom, since it can pivot up and down as well as back and forth. Figure 8-6 shows the ball and socket in three di erent forms. The illustration in the top-right corner is a type of joint found in radio-control airplanes. The ball is attached to a threaded stud that attaches to a control horn on a servo. The socket is attached to a push-rod and runs through the airplane to push and pull the control surfaces. The depth of the socket is just over half the diameter of the ball, so the opening in the socket is smaller than the diameter of the ball. Because of this, it snaps rmly into place around the ball.
CHAPTER 8 Joints
The bottom-left version is essentially the same. A brass ball is inserted into a ring-shaped socket that is curved to match the ball. The opening at both ends of the socket ring are smaller than the ball, and the middle opens up to match the curve of the balls. The ring snaps onto the ball. The ball may or may not have an attachment point. It may have a hole through it, where a shaft can slide or turn. Note that in this case you could rotate the shaft in the hole, as well as rotate the ball back and forth in its ring, giving three axes of rotation. The problem with these ball and socket joints is that they have a lot of friction; the t needs to be tight to keep the ball from falling out. There is a lot of contact between the ball and its socket, and this creates a lot of friction. A ball and socket give two degrees of rotation, so could we put together two single-axis joints in a way to simulate this Yes. The result is a universal joint, or U-joint.
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