Example Problem : Slider Crank (Relative Acceleration)
|Example Problem : Slider Crank (Relative Acceleration) |
|Shown at right is a slider crank mechanism. At the position shown, |[pic] |
|slider C moves upward with vC = 2 fps and aC = 1 fps2. Determine the | |
|angular accelerations of links BC ( αBC ) and AB ( αAB ). | |
|Step 1: Velocity Analysis (to find ω’s) | |
|[pic] | |
|Write x and y scalar equations: | |
|[pic] [pic] ωAB cos30 = 0 + 2ωBC·cos 45 (1) | |
|[pic] [pic] ωAB sin30 = 2 - 2ωBC·sin 45 (2) | |
| | |
| |Solve: ωAB = 1.464 rad/sec [pic] |
| |ωBC = 0.897 rad/sec [pic] |
|Step 2: Write the Relative Acceleration Equation: Assume [pic] directions for both αAB and αBC. Because point B moves in a circle about A, |
|aB has two acceleration components. Because B also moves in a circle relative to C (on link BC), the aB/C term also has two acceleration |
|components. |
|[pic] |
|Write x and y scalar equations: (Here we have 5 vectors to resolve into x and y components): |
|[pic] [pic] αAB cos 30 + 2.14 cos 60 = 0 – 1.61 cos 45 + 2αBC·cos 45 (1) |
|[pic] [pic] αAB sin 30 - 2.14 sin 60 = 1 – 1.61 sin 45 - 2αBC·sin 45 (2) |
|Solve: αAB = -0.361 rad/sec2 as drawn = αAB = 0.361 rad/sec2 [pic] |
|αBC = 1.34 rad/sec2 [pic] |
| |
|Because αBC acts in the same direction as ωBC, then ωBC is increasing. |
|Because αAB acts in the opposite direction as ωAB, then ωAB is decreasing. |
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