DIY 3D Speaker Scanner - the Mathematics and Everything Else

[Few]

I was trying to imagine ways to minimize the sound-reflecting surfaces in the mic support structure. Along the way it occurred to me that the rigidity of a conventional CNC router isn't necessary if the goal is to position a microphone with no forces acting on it.

So maybe the approach used in the Maslow CNC router could be adapted. The core idea is that the object to be positioned (here the measurement mic) is suspended by a couple pairs of suspension cables. The cables are retracted or deployed by stepper motor-controlled pulleys mounted on tracks mounted on the ceiling. This allows the mic to be positioned anywhere in the plane containing the two pulleys, limited by their spacing. That plane could be moved closer to or farther from the speaker by translating the stepper-pulley systems along the ceiling tracks. In an attempt to convey the nature of the motion, I drew up a sketch that shows the mic in two of the possible positions.

Obviously the software driving the stepper motor controller would have to do a little trigonometry to convert the desired mic position to pulley rotation. I've also left out some practical details that would have to be ironed out so that the mic moves as intended, but I hope the basic idea is clear. The approach doesn't require many parts so if the idea turns out to be a bust at least there wouldn't be a lot of money invested!

Few

 

[NTK]

I was trying to imagine ways to minimize the sound-reflecting surfaces in the mic support structure. Along the way it occurred to me that the rigidity of a conventional CNC router isn't necessary if the goal is to position a microphone with no forces acting on it.

So maybe the approach used in the Maslow CNC router could be adapted. The core idea is that the object to be positioned (here the measurement mic) is suspended by a couple pairs of suspension cables. The cables are retracted or deployed by stepper motor-controlled pulleys mounted on tracks mounted on the ceiling. This allows the mic to be positioned anywhere in the plane containing the two pulleys, limited by their spacing. That plane could be moved closer to or farther from the speaker by translating the stepper-pulley systems along the ceiling tracks. In an attempt to convey the nature of the motion, I drew up a sketch that shows the mic in two of the possible positions.

Obviously the software driving the stepper motor controller would have to do a little trigonometry to convert the desired mic position to pulley rotation. I've also left out some practical details that would have to be ironed out so that the mic moves as intended, but I hope the basic idea is clear. The approach doesn't require many parts so if the idea turns out to be a bust at least there wouldn't be a lot of money invested!

Few

For positioning in a flat plane, this should work. One thing you need to watch out is that your proposal as shown has no rigidity in the speaker axis direction, and the mic can swing back and forth in that direction. The CNC router in the video rests on the board being cut, and it provides a constraint in one direction. I am sure you can figure out a away to provide this constraint so I won't give my opinion (at least for the time being)

I think it will be useful for me to run some simulations to get a feel for what kind of accuracy we would get from measuring on one plane only. Hopefully I can get some done in the next week or two, but no promise

 

[Few]

Yeah, I've been pondering the unconstrained axis. I'll avoid embarrassing myself by posting the half-baked ideas I've had so far! I agree that it seems like a solvable problem. If it is, then motion along the ceiling tracks could be motorized as well. In that case measurements would not be constrained to a plane.

In the scheme I sketched, though, the mic's orientation is fixed so it would not always aim at the speaker. I was going to say that's a problem that has to be addressed, but if the mic's orientation changes as it does in the Klippel system, doesn't it respond differently to the reflections from the room's walls? It seems like that would cause its own problems. Maybe that was addressed in a previous post; I haven't gone back to reread the entire thread recently.

Few

 

[NTK]

No need to feel embarrassed. The rule for brainstorm is that there is no stupid idea

The mic in the Klippel system is also fixed (it only always point at the rotational axis and does not tilt up/down). With reflections, sound can come from any and all directions, so I think the system/method depends on the onmi behavior of the measurement mic.

 

[bigjacko]

Maybe you can add a third motor and pulley to control the third axis. If you add the third one the position will get a bit more complex, but there should already be a way to calculate it somewhere, should be related to mechatronic. Or you like some challenge derive it yourself.

Edit: I just spend a bit of time thinking about this problem and found the solution to the three motor is actually very easy. Solution is as follow : (1) find the position in x y z of the measurement point (2) get the distance to the three motor in x y z (3) calculate the length of the rope needed by trigonometry (4) if you got the three rope length correct, the microphone will be at the right place. So in the end we only need to calculate the length of the rope using trigonometry.

 

[somebodyelse]

That's an interesting solution. I think there will be some mechanical challenges at the mic end for precision placement, but they may not be insurmountable. Mic vertical below the suspension point, light flexible cable hanging from above, and use the mic's 90 degree calibration.

 

[NTK]

For the high achievers, see the NIST Robocrane, a 6-DOF implementation (giving full positional and attitude control) which basically is a variation of the Stewart platform. The math is already done.
https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=820409

 

[Few]

And the ubiquitous SkyCam:

 

[somebodyelse]

MachineKit / LinuxCNC already has kinematics for tripod and hexapod, but Marlin and GRBL don't unless I've missed something. There may be other freely available implementations (ROS?)

 

[No. 5]

My thought follows along the line of your idea by making measurements on flat planes. Say we make measurements on a plane in front of the speaker.

If flat measurement planes work, it seems to me that the system could be adapted to measure raw drivers (or in wall/soffit mounted speakers). That would be very useful for DIY'ers.

 

[NTK]

If flat measurement planes work, it seems to me that the system could be adapted to measure raw drivers (or in wall/soffit mounted speakers). That would be very useful for DIY'ers.

I think using the system as proposed by @Few (post #121), but with 4 cables, two connecting to the front of the measurement mic and two connecting to its rear, we should be able to position and orient the mic to measure in hemi-spherical surfaces. See the 2π scan in the figure below. (Source: https://www.klippel.de/fileadmin/klippel/Files/News/ALMA2016 - The infinite baffle.pdf )

I'll get my behind moving to run some simulations to get a feel as to how well this may work.

 

[Few]

Googling to follow up on the useful posts has left me, at least for the moment, thinking that something like the 6-cable design NTK highlighted has the most promise. Videos of DIY SkyCams make it clear that without gyroscopes or gimbals the platform suspended by 3 cables wobbles all over the place. The 6-cable design is kinematic so it fully constrains the position and orientation. If the NIST folks could use it to manipulate a chainsaw in action it can probably handle a microphone.

The NIST Spider robot requires 6 motors to control the 6 cables for full control. I’ve not done a thorough job working through the vectors and matrices in the NIST paper NTK linked to, but my gut (always dangerous) says that if the mic orientation could remain fixed, and only its position were varied, independent control of all 6 cables might not be necessary. I think the 6 cables are required but perhaps just 3 motors would be sufficient? I stand ready to be corrected...

Few

Edit: Oops! Two posts, passing in the ether. I hadn’t seen NTK’s post before launching my own. I’ll leave it as it was, nonetheless.

 

[bigjacko]

There are two ways to control the pivot angle of microphone. First is use a plane like plate and control the cable length. Second is make an end for those 3 or 6 cables, put a short cable at that end and tie the microphone on the short cable, but we will need another motor to control the pivot angle. So the second way does not have to do the calculation for the flat plane, but will still have to do the calculation of the pivot angle and rotate angle. Rotate angle is rotation used for doing horizontal measurements, pivot angle is for vertical measurements.

 

[Few]

Second is make an end for those 3 or 6 cables, put a short cable at that end and tie the microphone on the short cable

I'm not sure I'm correctly visualizing your suggestion. If the mic is suspended from a single cable dangling off the point where the other cables come together, what prevents the mic from wobbling, which would cause uncertainty in the capsule's location? I'm probably just misinterpreting your description--can you clarify?

Few

 

[bigjacko]

I'm not sure I'm correctly visualizing your suggestion. If the mic is suspended from a single cable dangling off the point where the other cables come together, what prevents the mic from wobbling, which would cause uncertainty in the capsule's location? I'm probably just misinterpreting your description--can you clarify?

Few

You are right about the visualization, this way the microphone will wobble, we will need to figure out how to damp it. If going this route we may need another cable at the rear to control the pivot angle. For damping can we use some kind of rubbber tubing outside of the cable so the rubber can damp the cable. This whole thing is just an idea, because a platform may introduce sound reflection.

 

[Few]

No problem bigjacko--I just wanted to be sure I wasn't misinterpreting.

Further digging turned up a DIY cable crane project that incorporates a nifty trick. With just three motors and 6 cables Tom demonstrates (by stacking six empty Bud Light cans...) nice stable and controllable motion. The trick is to run two cables from each capstan, but vertically displace them from each other so that they are always parallel. He emphasizes that stable motion requires that each set of three cables must meet at a point at the business end, rather than connect to the corners of a rigid platform. He reports that the motion is less reliable at the limits of the working volume, but the volume can be made as large as necessary. I've tried to incorporate the idea in an updated sketch; the long tracks on the ceilings aren't necessary in this scheme. I just didn't bother to erase them.

Now the trick is to find a rigid but acoustically transparent post to mount the mic to! I don't have any aerogel in my scrounge jar.

 

[bigjacko]

@Few That's interesting idea. The person found the stick way is genius haha. I am not familiar with aerogel but know that it is like a glass containing air, does it has same acoustic property as air? We will also come up with a way to pivot and rotate the microphone.

 

[Few]

Glad you find the idea worthwhile. I just threw aerogel in there because I couldn’t come up with a way to include graphene. Nothing counts these days without graphene.... Aerogel is pretty cool stuff, though. It comes in a wide variety of forms, but the rigid ones can be used as a superinsulator. They even use it to capture particles in space without damaging them. I was trying to think of a solid material with very low acoustic impedance and on a hunch looked up aerogel. Sure enough, it’s been studied and found to have very low acoustic impedance.

All that said, I’m confident a less whimsical approach can be found to minimize reflections off the post or whatever is used for that purpose. Maybe just a thin triangular wedge of acoustic foam would get the job done. I was surprised how big a glitch my microphone stand causes in impulse response measurements even though the stand is about 1 m behind the mic capsule. It took me a bit to nail down the problem because it didn’t occur to me that something with less than a 1 inch profile, located 1 m away, could cause so much trouble.

Because microphones aren’t heavy, I was imagining something like low-stretch fishing line made of polyamide as the ”cables.” I haven’t really researched it yet, though. Perhaps Kevlar thread? In any case, it can have a pretty tiny cross-section so I don’t think the cables will cause acoustic problems.

Are there any stepper motor experts in the loop? I’ve found with limited experience that some stepper-driver combinations create a fair bit of acoustic noise even when stationary—not good for this application. Is there a way to minimize that problem? I’d be willing to step out of the theoretical realm and take some baby-steps toward implementing a prototype if I can gain some confidence that I’ll not get stuck in a cul de sac. I’m encouraged that moving a mic along an arbitrarily defined 3D surface doesn’t look overly difficult, and I would love to find a way to simultaneously remove reflections from my speaker measurements, and acquire useful directivity information.

Few

 

[dc655321]

I’ve found with limited experience that some stepper-driver combinations create a fair bit of acoustic noise even when stationary—not good for this application. Is there a way to minimize that problem?

High order micro-stepping drives may smooth some of the discrete noise. Adding some well placed mass damping may also help. Or, there are always servo motors that would work here too.

 

[somebodyelse]

Have a look at Trinamic's stepper drivers. The Silent Stepstick is a widely available implementation, and there's plenty of open code for driving them as they've become common on 3d printer driver boards. I don't think any of the common 3d printer code has the right kinematics though - see LinuxCNC or MachineKit for that.
I was thinking of dyneema kite lines, but only because I've got some - the strength would be overkill, and something smaller would probably be better on the drum. A high moduilus fishing line seems ideal.