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## Parallel Robot kinematics

i would like to have a help in calculating parallel robot inverse kinematics since i do have to implement a high speed pick and place robot any suggestions?? its 4 DOF

2. ## Re: Parallel Robot kinematics

What, specifically, do you need help with? Do you have a sketch of the links and actuators?

In general, if you have 4 DOF but want to constrain 6 DOF (position + orientation) you're screwed, unless the axes are designed to fix certain DOF (i e, parallel arms keeping a surface perpendicular.)

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## Re: Parallel Robot kinematics

Originally Posted by jwatte
What, specifically, do you need help with? Do you have a sketch of the links and actuators?

In general, if you have 4 DOF but want to constrain 6 DOF (position + orientation) you're screwed, unless the axes are designed to fix certain DOF (i e, parallel arms keeping a surface perpendicular.)

here is the robot 3 motors on every arm end at the top and one motor over the endeffector to achieve rotation i dont know the suitable inverse kinematics since there are a lot of theories on internet

4. ## Re: Parallel Robot kinematics

So, at the top there are three single-axis rotational joints, each set 120 degrees apart. They each establish a plane within which each "femur" rotates.

Then each femur has a parallel linkage of ball joint to ball joint for the femur. This in theory gives you two degrees of freedom (three for ball joint, remove one for parallel arms) but the arms will likely flex a bit (plus there's play in the ball joints.) The tibias are tied with the ball joints at the shared "toe." Your hope is that the freedoms of each of the separate tibias are constrained such that they cancel out and end with a parallel 3D position of the end "toe."

You can solve this with high school trigonometry, viewing each assembly as a two-bone IK setup, solving a quadratic equation and using the cosine rule to figure out the angle to drive each motor to to position its effector. It would be slightly easier to visualize using first-year university math as linear algebra. That would also let you write out a single system of equations to solve.

Look at each leg in isolation. Fixed inputs are length of femur, length of tibia projected to the femur movement plane, after compensating for sideways movement shorting it, and relative projected position of end effector compared to femur axis of rotation position. Do this for each of the three bones (projecting to successive 120 degree offset planes.) Solve each of the three two-bone IK systems. Done!

For simplicity, you want to consider the centerpoints of the ball joints of each parallel linkage as "the point" rather than trying to do math for each arm of that linkage. This means that you're positioning the centerpoint of the two ball joints of the "toe" as the input to the equation. Similarly, you want to make sure that the three target positions are pre-arranged to the exact positions they'll need to have for a flat effector pose.

Is this enough for you to work it out? What level of math have you studied?

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## Re: Parallel Robot kinematics

i reached numerical analysis as i am in my graduation project but i never learned about parallel robot i learned analysis of serial only but thanks for your help i will do my best to apply what you told me and i hope i reach it fast

6. ## Re: Parallel Robot kinematics

You say numerical analysis, but do you have trigonometry? Linear algebra? Calculus?

Assuming you know how to project from 3D to 2D (project along plane normals) the what you do is calculate the 3D position you want each linkage to be at for the center puck, then you project to the 2D planes for each of the three linkages, then you solve each linkage on its own for that target position. The only difference compared to "plain" 2-bone IK is that the length of the outer bone "changes" (more accurately, the projected length of the bone on the 2D plane for one motor changes.) Because all you need is the angle of the top motor/joint, you just have to assume that the rest will work out (which they should, if everything is accurate and tight.)

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## Re: Parallel Robot kinematics

i have all the following mathematics and i can also use matlab to calculate for me but i was need a starting point

8. ## Re: Parallel Robot kinematics

OK. Construct three planes, each with the axis of rotation of the top motors as their normal, going through the center of rotation of the top joint. Place origin of 3D space in top center of the bot, so it will be in the center of rotation for each motor.

Now, figure out where you want the end effector positioned in 3D space. You can calculate the center of the effector, as it will project straight through the linkage to the appropriate 2D plane for each linkage.

Now, project center-of-effector to the 2D plane. This gives you a target point for a 2 bone IK. The length of the first bone is known. The length of the second bone is the projected length of the second linkage. You can find this using Pythagoras, as you know how far the target joint is from the plane (it should be along the plane normal, parallel to the distance of the center of the effector.) So, actual length = sqrt(length*length - offset*offset) With two known lengths, and a known target point in the plane, you can use the triangle cosine formula to solve the 2-bone IK.

Now, in that solution, the angle of the top servo will come out; this is your control output. Repeat this for each of the three planes, to get the angle for each of the three servos.

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## Re: Parallel Robot kinematics

thank you for much information i will start to try to calculate it

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