Need mechanism for connect from handle to controlled object (please see pic)

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SUMMARY

The discussion focuses on creating a mechanism to connect a handle to a controlled object, requiring a movement ratio where a 10cm handle movement translates to a 25-30cm object movement. Participants suggest using a simple and reliable rod or bar connection instead of gears or wires. A mechanical telescopic rod or a slotted vertical lever arrangement is proposed, with an emphasis on a pulley system that utilizes fishline to achieve the desired motion ratio. The consensus is that a pulley arrangement with a 2:1 or 3:1 ratio is the most effective solution.

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  • Understanding of mechanical linkages and motion ratios
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Mechanical engineers, product designers, hobbyists in robotics, and anyone interested in creating efficient mechanical linkages for controlled motion applications.

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handle.png
Please see the above picture, I need a mechanism to connect handle to a controlled object below. While the handle moves from a to b (~10cm) the object needs to move from c to d (about 25 - 30 cm) and when handle moves back from b to a, the object needs to moves back from d to c. They are both restricted in a box 3 to 4 cm high.

The mechanism should be simple and reliable for repeat operation. So I prefer rod, bar connection over gear or wire link.

Is there something like mechanical telescopic rod on the market where you can extend the whole rod length by moving a little control distance?
 
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How about a slotted vertical lever arrangement, pivoted between the two paths such that the motion of the lower end is 2 or 3 times the motion of the upper end?
 
In this case, I honestly can't think of anything better than just running some fishline through a 2:1 or 3:1 (depending upon what you end up having as your actual final path) pulley arrangement.
A couple of wheels, a couple of knots, and Bob's your uncle.
 

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