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I am trying to build a rig described on the scheme:
I want the IK solution to conform automatically to settings of both slider manipulators (path constraints) and to the movement of the part to the left (to which joints 1 and 6 are linked / constrained).
Part I'm having problems with is highlighted in red.
My approach was to have such a hierarchy: one HD IK chain from joint 1 to 4 (1-2-3-4) and another one from 2 to 6 (2-5-6).
But I don't know:
a. How to incorporate the path which joint 3 should follow.
b. How to make bone 2-3 stretchy only to adjust joint 3 to it's desired position on the path and not to stretch because of the IK solution.
c. How to make angle between bones 2-5 and 2-3 change only to adjust joint 3 to it's desired position on the path and not to change because of the IK solution.
d. How to make joints 3, 4 and 6 to strictly "sit" in their positions and not to deviate from their positions. When I link IK end effectors to dummies and add position constraints everything becomes a mess(((...
@andrij.byelyayev I am trying to understand the kinematic action of your mechanism before trying to determine appropriate rigging. Are you familiar with Gruebler's Equation? It can be used to determine the degrees of freedom given the number of links and joints. The simple form is
3* (L - 1) - 2 * J = degrees of freedom.
where, L = number of links and J = number of joints.
For example, A 4-bar linkage (3 *(4-1)-2*4 =1 ) has 1 DoF while a truss (L=3, J = 3) = 0 DoF (a structure not a mechanism).
For your mechanism, you choose a location for point #4 so we can consider it fixed (grounded). Point #3 is fixed relative to the pink object for a specific configuration. In this case we have 6 links and 6 joints or 3 degrees of freedom. Since pink cannot rotate (is this true?) then we can subtract 1 DoF yielding 2 DoF. Link 4-3 angle of rotation is 1 DoF . The link chain 1 - 2 -5 -6 is a four bar linkage with 1 DoF but none of its links are grounded. Since the translation and rotation of 1-2 in constrained by it path the result is 1 DoF.
To be clear, you want to move the object contain 1-2 along a path. Its position on the path determines its location AND rotation.
In the attached file I created a crude model of the linkage. It does not do what you want but you can rotate the crank link (arrow) and the parallelogram linkage will articulate to an orientation you want. Then move the rectangle to a where you want and the rest of the linkage will follow. To effect the change caused by moving 3 in its slot just move the IK goal relative to the rectangle. The change of the position for 4 is achieved by changing the position of Bone001.
The position of pink is a function of the position and rotation of peach. I think this is best controlled via an expression or transform script controller.
I would write a transform script to control the location of the pink object based on the position and rotation of the Moving Part with a feature to move the location of point 3 based on a slider position.
I will not be able to give this any time for a couple of days but let me know if this is what you seek to do.
@domo.spaji @leeminardi, Thank You!
Unfortunately, I'm recreating a machine from photos, and can't find any video of it's work.
Leaving aside the movement of the "moving part" and possibility to adjust joints 4 position (let's say they are grounded), I want to build a system, where "pink part" will be automatically positioned in right place, when I change the position of joint 3 in relation to it (in relation to bar 2-5).
The right place would be when 2 rules are met:
1. Joints 2 and 5 in new position will have same distance from joints 1 and 6 respectively (r1) so that:
1a. Bar 2-5 will stay parallel to 1-6;
2. Distance between joints 3 and 4 in new position will stay the same (r2)
I'm new to scripting or expressions, so I do knot know for now how to write this "system of equations" to work in 3DS MAX...
The fact that I can't solve it with IK is pretty disappointing(..
@domo.spaji @leeminardi
Hope this image will finally make everything clear.
Left and right columns represent moving (peach) part extreme positions.
Rows represent the correct position of the tricky (pink) part for four extreme positions of joints 3 and 4 on their paths (which I want to have the ability to control by sliding manipulators)
I've drawn this in CAD, so I'm sure such system (mechanism) is possible.
Still can't recreate it in MAX(...
I'm almost there, but not at all still.
I've set up an IK chain with two perpendicular bones (3A and A5) instead of one bone 3-5
to easily control 5 position relative to 3 by changing bone A-5 X.POS with upper slider manipulator.
Bone A-5 rotational joints are OFF, so that it stays perpendicular to 3-A
Bone 4-3 (root bone) is linked to a dummy that is path constrained and controlled by lower slider manipulator.
The problem is: I can't make IK solver keep bone A-3 parallel to 1-6 (as it should) and search for a solution (position of joints 3, A and 5) within this limitation.
If only I could do so, the problem would be solved.
I also understand that from the mathematical point of view I need to find two vector angles:
<1-6-5 (between 1-6 and 5-6) and <3-4-6 (between 3-4 and 6-4) for which vector sum (4-3)+(3-5)+(5-6)=(4-6),
which is possible to solve as I know because all the lengths of vectors are known and angle of vector (5-3) is also known.
Maybe, @leeminardi you can give some advice on how to write this with MAXScript, or, maybe, a tutorial on how to do so...
@andrij.byelyayev I think I have a solution!
To review, given the following:
you would like to move and/or rotate Moving Part and have Tricky Part move and rotate accordingly. The rig should also work if the location of joint 3 on Tricky Part and joint 4 on Fixed Part are moved. In addition, Link 1-2, Tricky Part (2-5), link 5-6 and Moving Part (1-6) form a parallelogram linkage that ensures that the rotation of Tricky Part is the same as Moving Part.
Assuming that Joint 3 and 4 are temporarily fixed, we know that we can determine the location of joint3 if we know the angle that line 5-6 forms with a horizontal reference line. A valid solution will place joint3 a distance from joint4 that is equal to the length of line 3-4. I created a numerical method solution (i.e., a solver) to determine the angle of link 5-6.
The transform script for Tricky Part is:
The complete code is:
-- Calculate position and orientation of Tricky Part
-- that will have Joint3 a disatnce L34 from Joint4.
L56 = 228.35
L34 = 220
g1 = 0 -- lower limit angle guess L34 from Joint #4
g2 = 90 -- upper limit angle guess
gm = (g1 + g2)/2. -- mid angle guess
pt4 = Joint4pos * FixedPartT -- pivot point of link 3_4
m = copy MPT -- make independent copy of Moving Part's transform
for i = 1 to 10 do -- take 10 steps to converge to a solution
(
-- find the location of pivot point #3 for the 3 guesses
p1 = Joint8Pos * MPT + L56 * [cos(g1), 0 , sin(g1)]
p2 = Joint8Pos * MPT + L56 * [cos(g2), 0 , sin(g2)]
pm = Joint8Pos * MPT + L56 * [cos(gm), 0 , sin(gm)]
m.pos = p1
local v1 = Joint3Pos * m
m.pos = p2
v2 = Joint3Pos * m
m.pos = pm
vm = Joint3Pos * m
-- computer distances for the 3 guesses
d1 = length(pt4 - v1)
d2 = length(pt4 - v2)
dm = length(pt4 - vm)
if dm > L34 then -- determine which 2 guesses bracket solution
( g2 = gm
)
else
( g1 = gm
)
gm = (g1 + g2)/2. -- compute new middle guess value
i = i + 1
)-- end for ------
m.pos = pm
m -- position Trick Part to new location
The code works as follow. After the length of links 3-4 and 5-6 are defined, three initial guesses are made for the angle of link 5-6. They are g1 = 0°, g2 = 90° and midway guess gm = (g1 + g2)/2 = 45°.
The distance from joint 3 to joint4 for the three cases is then compared to the goal distance, the length of link 3-4. If the distance for angle gm is greater than link 3-4 (L34) then the upper bound is changed to gm (g2 = gm). if not, the lower bound is changed to gm (g1 = gm) and gm is redefine as the midway angle between the new set of g1 and g2. The process can be repeated until a desired level of precision is found. For now, I just limited the search to 10 iterations which works fairly well (I ran out of energy). I can adjust this later.
Once we know the location of Joint3 a LookAt contrainst is used to rotate link 3-4 and link 1-22 to their correct angles.
Note that joints 3 and 4 can be moved within their slots by simply changing to the local coordinate system and then moving these joints in the desired direction. Their position could of course be controlled by a Slider Manipulator.
There were many challenges in getting this solution.
- The original geometry behaved badly! I don't know why but my only solution was to rebuild the major parts.
- The were too many constraints already applied to objects. It's best to start with clean, unconstrained objects (e.g., no basic or inherit locks), IK constraints, etc.
- Poor choices for pivots. With links it is best to have a local principal axis that is in the direction of the link.
- I had the statement
m = MPTin my code where MPT is the Transform matrix for Moving Part. Later in the code I modify the matrix m not realizing that in doing so MPT is also modified! I had assumed that, as with most other programming languages, modifying m does not affect MPT. I was wrong and discovered that m in this case was essentially an instance of MPT. This problem was fixed with the statement
m = copy MPT
Very simple once you know what to look for!
To see the action move and or rotate Moving Part in the attached file. The object could be linked to a path with follow checked and the part would move and rotate as the percent-along value is changed thus meeting your original goal. As noted, you can move joints 3 and 4.
@leeminardi, everything is clear so far, except the different local coordinate systems for different objects was a bit confusing. But I'm sure, there will be more questions as I'll tackle new challenges.
What I was trying to do (and did with your great help) was to make this machine work absolutely realistically, so that I can adjust it as in real life and it will work correctly whichever rocking pattern I choose.
As you can see, there are four "manipulators", which change the way rocking motion is translated to other parts.
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