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Pre-Calc Exam Notes 18

# Pre-Calc Exam Notes 18 - θ with the line OA The...

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18 Chapter 1 Right Triangle Trigonometry §1.3 Example1.18 A slider-crank mechanism is shown in Figure 1.3.2 below. As the piston moves downward the con- necting rod rotates the crank in the clockwise direction, as indicated. connecting rod b A B O crank a c C r θ piston Figure 1.3.2 Slider-crank mechanism The point A is the center of the connecting rod’s wrist pin and only moves vertically. The point B is the center of the crank pin and moves around a circle of radius r centered at the point O , which is directly below A and does not move. As the crank rotates it makes an angle
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Unformatted text preview: θ with the line OA . The instantaneous center of rotation of the connecting rod at a given time is the point C where the horizontal line through A intersects the extended line through O and B . From Figure 1.3.2 we see that ∠ OAC = 90 ◦ , and we let a = AC , b = AB , and c = BC . In the exercises you will show that for ◦ < θ < 90 ◦ , c = r b 2 − r 2 sin 2 θ cos θ and a = r sin θ + r b 2 − r 2 sin 2 θ tan θ ....
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