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I'm a programmer. I had a tiny amount of experience building robots in college a few years ago, but haven't done anything since.

I'd like to build a robot that can move around my house, pick items up and put them down... IE, a robot that could get items out of the dishwasher and put them away.

I was thinking it would have a square base with a wheel at each corner for moving around the floor, a scissor jack so it can adjust its height (I'm hoping to be able to be able to move between 1 foot tall and 7 feet tall), and then a scissor jack at the top for moving a gripper towards or away from it (between a couple of inches and 3 feet away).

Are two scissor jacks actually what I want? It seems like 90+% of robots with grippers go with arms instead, but it seems to me that those are more complicated and would be less precise. I have no robotic experience beyond little car like things - I've never built one with any sort of gripper or actuator, so advise would be much appreciated. (Huh - there's not even a tag for scissor or jack... what do you guys call them?)

Also... do people normally build these parts themselves, or do they buy them? I've searched around but I can't find any scissor jack kit or anything like that. If I need to build it myself... how would I do that? What would I build it out of?

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The reason most robots use arms is because they are simple and easier to do inverse kinematics on than other mechanisms. Also you don't want to do a 7ft scissor lift because you will end up needing a lot of torque and your control suffers from the change in extension rate based on the height. You will probably end up making your own arm because buying premade arms get expensive.

With respect to your driveline, make sure your base is not too small. If you raise something to 7 ft you start to have center of gravity (CG) problems given your base is probably small for use in a house. Consider the robot on an incline plane. All your robot needs to tip is for your CG to move beyond your lowest wheel which is your lowest contact point. For example if your CG moves to 4.5 ft when your lift is 7 ft height and you have a 2ftx2ft square chassis then your robot will tip at an incline of ~12.5 degrees. This means that if it manages to tilt 12.5 degrees from something like it being bumped then it will fall over. Also if it's going to be autonomous you might want to avoid skid steering because it makes encoder readings worst.

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a robot that could get items out of the dishwasher and put them away

This is an active research topic. Toyota has a whole division working on assistive robotics, close to Stanford in Palo Alto. It is by no means a solved problem.

That being said, scissors are a fine way to guide motion in a single dimension, when you can afford the additional size perpendicular to the axis of motion. Scissors expand sideways a lot when they are close to the minimum extension point. Also, the backlash in the scissor joints adds up, so a four-joint scissors has four times as much backlash as a single-joint mechanism. Backlash in turn adds to flex and imprecision in movement.

If you're running this in your home, also consider the pinching hazard for pet tails, child fingers, and the occasional forgetful owner.

Another option, that is often used, and that uses less space, is a linear actuator. This can be as simple as a worm screw driven by a gear motor or stepper, and some kind of sensor. Open loop stepper counts, encoder motor counts, potentiometer, distance sensor, ... plus a homing / zero sensor / limit switch. Add parallel linear rails/rods with appropriate bearings and you get a high-precision, high-strength assembly.

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