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Try This: The four-bar link provides a way to move a link parallel to a base (Fig. 14-10). In this accounting, the base is considered a bar creating a exible box.
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Fig. 14-9.
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Fig. 14-10.
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Two of these parallel links, plus the gearing system from Fig. 14-8, can make a parallel-gripping hand (Fig. 14-11). The parallel mechanism can be turned in the other direction for a narrower grasp (Fig. 14-12). A gearing arrangement can replace the bars to provide parallel motion, though you then need to contend with backlash. Figure 14-13 shows geared parallel motion. The arm is driven from the side by an additional link.
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Fig. 14-11.
Parallel gripper.
Fig. 14-12.
Another parallel gripper.
Shaping Motion
Fig. 14-13.
Geared parallel motion.
FOUR-BAR LINKAGE
The four-bar linkage can be used for more than simple parallel motion. By changing the length of the four links you can program the linkage to start in one position and end in another. First we need to name the links for easy reference. The base or stationary bar is the ground bar. The link whose motion we are designing is the coupler bar. The other two links are the crank and the follower. A crank is the powered link, and a follower is the unpowered link. The rst thing to do is to decide where the coupler bar must go. Only the starting and ending positions are signi cant, so we draw these into place relative to the ground bar (Fig. 14-14). Let s call one end of the coupler A and the other end B. Draw a large circle centered on the start and end positions of end A. The circles need to be large enough so that they overlap, as shown in Fig. 14-15. Now draw a line through the two points where the circles overlap. Where this line crosses the ground bar is where the follower is attached. The other end of the follower is, of course, attached at point A on the coupler. The length of the follower is the distance from the ground pivot to point A. This procedure is repeated with point B (Fig. 14-16).
Shaping Motion
Fig. 14-14.
Desired start and end position.
Fig. 14-15.
Locating the follower pivot.
Fig. 14-16.
Locating the crank pivot.
Shaping Motion
Fig. 14-17.
Complete four-bar linkage.
When you build this mechanism, it will reach the desired positions precisely, as shown in Fig. 14-17.
COMPLEX MOTIONS
Try This: The oscillator in Fig. 14-7 provides a smooth, reciprocal motion that looks something like Fig. 14-18. Coupling two cranks together to drive a follower link can provide a more complex, harmonic motion. One such mechanism is shown in Fig. 14-19. An estimate of its motion pro le is given in Fig. 14-20.
Fig. 14-18.
Reciprocal motion.
Shaping Motion
Fig. 14-19.
Harmonic linkage.
Fig. 14-20.
Harmonic motion.
Shaping Motion
Other Mechanisms
If you spend some time browsing through online patents, either via the Patent O ce (www.uspto.gov) or some other patent portal like Delphion (www.delphion.com, and yes they have a free version buried in there), you will see numerous clever and unique mechanisms to achieve many di erent mechanical goals. Some examples are illustrated here.
CARDAN GEAR
While the the crank-and-piston arrangment can create linear motion from rotation, the cardan gear does this in less space and with a completely di erent technique (Fig. 14-21). The cardan gear is actually two gears. The outside ring is a gear turned inside out and it provides a xed framework for the moving gear. The inside gear has exactly half as many teeth as the outside gear. A post positioned over one tooth of this inside gear follows a straight line. This post can be used to drive additional machinery.
Fig. 14-21. Cardan gear.
Shaping Motion
Fig. 14-22.
Quick-return.
QUICK-RETURN
Try This: A gear with a post on it can be used to drive other mechanisms; for example, in a quick-return (Fig. 14-22), the gear pushes the link back and forth. At the top of its arc the post moves the link slowly, along a large radius. At the bottom of its arc the post moves the link quickly since it is closer to the link s axis of rotation.
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