Explicação Case 4_PT.txt
They’re just two linkages attached with pins. The only design choices to make are the length of the arms, the angle of the pins, and the distance between the two tracks. You can adjust each of these to increase or decrease the range of motion for the end efector.
They’re actually surprisingly straightforward. Each of the carriage/arm assemblies has a fixed plane of motion, set by the fixed angle of the pin where the arm attaches. You just take the normal vector of that pin, plus the location along the track to get the equation for the three planes. Then you can actually just solve each of them independently, since they only depend on the location of the one specific carriage and the desired position of the end effector.
But how do you keep the system from oscillating from over correction?
Typically with a PID controller. Depending on the design requirements you’re trying to meet, you can tune the P, I, and D coefficients to change the behavior. To get rid of oscillation, you would bump up the D coefficient so the robot slows down as it approaches the target position.
The big benefit of the tripteron over the delta design is the linear control. That means no singularities to worry about, you have the same resolution and thrust characteristics everywhere in your work envelope and the forward and inverse kinematics are all trivial. It makes it very easy to work with. I was able to use a stock G-code interpreter and a spreadsheet to make the movements you see here.
Having fully orthogonal axes would have meant making a left and right hand version of each of the back carriage joints. By making those arms 90 degrees when projected onto the XY plane, those parts can be made identical and simply rotated 90 degrees from each other. It was just a little bit simpler to build that way.
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Explicação Case 4_PT.txt They’re just two linkages attached with pins. The only design choices to make are the length of the arms, the angle of the pins, and the distance between the two tracks. You can adjust each of these to increase or decrease the range of motion for the end efector.
They’re actually surprisingly straightforward. Each of the carriage/arm assemblies has a fixed plane of motion, set by the fixed angle of the pin where the arm attaches. You just take the normal vector of that pin, plus the location along the track to get the equation for the three planes. Then you can actually just solve each of them independently, since they only depend on the location of the one specific carriage and the desired position of the end effector.
But how do you keep the system from oscillating from over correction? Typically with a PID controller. Depending on the design requirements you’re trying to meet, you can tune the P, I, and D coefficients to change the behavior. To get rid of oscillation, you would bump up the D coefficient so the robot slows down as it approaches the target position.
The big benefit of the tripteron over the delta design is the linear control. That means no singularities to worry about, you have the same resolution and thrust characteristics everywhere in your work envelope and the forward and inverse kinematics are all trivial. It makes it very easy to work with. I was able to use a stock G-code interpreter and a spreadsheet to make the movements you see here.
Having fully orthogonal axes would have meant making a left and right hand version of each of the back carriage joints. By making those arms 90 degrees when projected onto the XY plane, those parts can be made identical and simply rotated 90 degrees from each other. It was just a little bit simpler to build that way.