RIGGING - Arms, hinge, spring, path constraints (willing to pay for help!)
the inter path was unnecessary ， you can get position of P0 P1 P2 , you can calculate angle γ ,and you know length of A B ， then using trigonometric functions to get the angle β，then you can get the matrix of B , set it
set the operate above as script expression ， it will set B automatic
the spring was just rigged with a scalable bone
Here's a first pass at one approach using a combination of LookAt contraints and a transform script.
The yellow link has a LookAT constraint to point towards the point on the path (pointB). Given the following:
we need to find the location of point3 that is at the intersection of a circle of radius D centered at the conection point of the yellow and white links, and a circle of radius L centered at point B. Since there are two intersection points there is the possibility of getting the wrong one. I used a numerical technique to find the intersection with an initial guess towards the bottom (i.e., -[0,D,0] or minus y). Ater the initial guess 10 more improved guesses are made giving fairly accurate results. As you will notice, the solution flips when the yellow link is vertical.
Point3 has the following transform script:
S = 142.54 -- length of yellow link
whitePivot = yellowLink.pos + yellowLink.row1 * S
D = 67.434 -- length of white link to connection point from red link
L = 58.2513 -- length of red link
g = whitePivot - [0,D,0]
for i = 1 to 10 do
(
g = normalize( g - pointB) * L + pointB
g = whitePivot + normalize(g - whitePivot) * D
)
matrix3 [1,0,0] [0,1,0] [0,0, 1] gThe red and whit links have LookAt constriants pointing toward Point3.
If you feel this approach has potential for you then post your geometry and I can try to address the flipping issue.
Here's an improved solution that doesn't flip Point 4 is linked to the yellow link and is used as the initial guess for the intersection of the two circles. To get its world coordinates it is mutiplied by the transorm for its parent, the yellow link. I've addded a spring which works well.
S = 142.54 -- length of yellow link
whitePivot = yellowLink.pos + yellowLink.row1 * S
D = 67.434 -- length of white link to connection point from red link
L = 58.2513 -- length of red link
g = pt4 * yellowLink
for i = 1 to 5 do
(
g = normalize( g - pointB) * L + pointB
g = whitePivot + normalize(g - whitePivot) * D
)
matrix3 [1,0,0] [0,1,0] [0,0, 1] g[EDIT 6/7/2025] The local x axis for each of the three links is in the long direction of the link. The red and white links have LooKAt constraints pointing their x axis towards point3.
@thefighting24th Michael,
I deleted the keyframing from your file and rigged it with the method I outlined above. I made a few changes to my script as your links used the local Z axis and I had assumed x. I changed the units to decimal inches from feet and inches as they were inconsistet with system units. Note that the white pivot in world coordinates is:
whitePivot = yellowCylinder.pos + yellowCylinder.row3 * sRow 3 of the yellowcylider transform is used for the z axis.
You can see in the script the values I used for S, D, and L.
I replaced the helix with a dynamic spring.
I appreciate the offer of compensation but I do this for the fun of it.
Rather than a zoom meeting, please outline any questions you may have.
Lee
The rigging works as follows:
- Point B has a position path constraint.
- Yellowcylinder (with a pivot at A) has a LookAt constraint pointing to B
- Whitepivot (at the end of yellowcylinder) is a distance S from A in the direction of yellowcylinder.
whitePivot = yellowCylinder.pos + yellowCylinder.row3 * s
Note that yellowCylinder.row3 is a unit vector pointing in the Z direction of yellowcylinder. - We need to determine the location of a point (Point3) that is a distance L from point B and a distance D from whitepivot. Point3 is therefore at the intersection of a circle of radius L centered at B and a circle of radius D centered at whitepivot. There are two possible solutions. We could use trig to determine the exact solution but using angles can get messy. I prefer using a numerical approach where a solution is guessed and then revised until a desired level of precision is achieved.
- The first guess (G1) for the location of point3 is at point4. This of course is way off so a new guess is made using G1 to locate guess 2 (G2) a distance L from B in the direction of B to G1.
- G2 is then used to make a better guess G3, a distance D from whitepivot in the direction from whitepivot toward G2.
- The guessing continues until an acceptable result is achieved. Rather than comparing recent guesses the program just does 10 guesses which from experience is good enough. The following code does these guesses.
g = pt4 * yellowLink
for i = 1 to 10 do
(
g = normalize( g - pointB) * L + pointB
g = whitePivot + normalize(g - whitePivot) * D
)
Once the location of Point3 is determined we can add LookAt constraints to the white and yellow cylinders. Using point4, which is linked to yellowcylinder, for the first guess ensures that we always converge to the desired intersection of the two circles.
Here's a version that I think yields constant angular velocity fot the yellow cylinder.
I replaced pointB with point Q (it was easier to debug using a new point) that has a path constraint to the curve.Line095. sQ is the % along value for pointQ. The vector w points in the direction of rotation for constant angular velocity. E.g., a frame 0 it is pointing straight up, at frame 50 it is point to the left. Vector v points from the center of rotation (pointA) to pointQ. The value of sQ starts at 0 and is incremented by delsQ up to a value of 1 UNLESS the dot product of v and w is greater than 0.999 (i.e., they are pointing in almost the same direction). If so the looping stops and the value for sQ has been found. The dot product of u and v yields the cosine of the angel between the two unit vectors. If u and v are pointing in exactly the same direction the angle is 0° and the cosine is 1.000. Steping through values of sQ starting at 0.0 unti a solution was found was easier to program then doing a bisectional search as I used in the trolley boom tutorial.
Here's the script for pointQ
sQ global -- % along vlue for pointQ
sQfinal global -- % along value for final position of pointQ
w global -- vector of contant angular velocity
frameStart = 0
frameEnd = 200
totalFrames = frameEnd - FrameStart
delsQ = (1. / totalFrames)
flag = true
ang = -1 * F / totalFrames * 360
w = [sin(ang), 0, cos(ang)]
for sQ = 0 to 1.0 by delsQ while flag do
(
ptQ = (interpCurve3D curve 1 sQ)
v = normalize(ptQ - ptA) -- vector A to Q
dot_vw = (dot v w)
if (dot_vw > 0.999) then
(
flag = false
sqFinal = sQ
)
)
sQFinal 
I'm traveling for the next few days and will not have access to my CAD PC.
