You will need these common tools for construction:
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Drill, ideally a cordless variable-speed reversible drill.
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Twist drill bits up to 1/4", and optionally a 17/64" bit.
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Phillips head bit.
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Square: a try-square, framing square, or speed square.
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Saw: a table saw or chop saw is good, but a saber saw or even a handsaw will work if you're careful.
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Clamps.
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Vise.
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Shoe rasp.
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Scissors, needlenose pliers, wire cutters.
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razor knife / box cutter.
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Adjustable crescent wrench for bolt heads and bike axle nuts.
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marking pen.
You may also need these less common tools:
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Step drill bit that includes a 13/32" step, for enlarging a hole in a metal angle to receive an axle.
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For making flanges from plastic bottles, a 1-3/8" hole saw for your drill.
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Bike wheel cone wrench. Jaw width depends on the wheel -- it might be 13, 14, 15, or 16 mm.