I am making a procedural animation of a worm. I have already something working:

enter image description here

(the green dot is the position Target, purple and red are the Head and the Tail of the Worm)

I would like to add another dot in the center of the Worm to simulate the middle body waving up and down while Head and Tail are moving like this:

enter image description here

I thought that it was going to be easy using some kind of 2D joint, but I tried several and I was not able to find a good result.

I was also thinking that maybe I have to make some trigonometry to calculate the possible positions of Center:

enter image description here

Before I over-engineer the solution what would be your approach to solve this?

  • 1
    \$\begingroup\$ It seems your looking for inverse kinematics. Here is a video that might help: youtube.com/watch?v=qqOAzn05fvk. This tutorial is for 3d but it can easily be changed for 2d. \$\endgroup\$
    – Simonster
    Commented Mar 30, 2021 at 17:55
  • \$\begingroup\$ @Simonster This helped, I'll use it if my worm becomes more complex :) \$\endgroup\$
    – fguillen
    Commented Mar 30, 2021 at 18:39

1 Answer 1


My final approach has been using basic trigonometry:

enter image description here

I have a and b I was just needing to calculate c:

void MoveCenter()
    float a = maxDistance / 2.0f;
    float b = Vector3.Distance(head.position, tail.position) / 2.0f;
    float c = Mathf.Sqrt(Mathf.Pow(a, 2.0f) - Mathf.Pow(b, 2.0f));

    Vector3 headTailCenterPosition = (head.position + tail.position) / 2.0f;
    Vector3 centerTargetPosition = new Vector3(headTailCenterPosition.x, headTailCenterPosition.y + c, headTailCenterPosition.z);

    center.position = Vector3.MoveTowards(center.position, centerTargetPosition, speed * Time.deltaTime);

The result:

enter image description here


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