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Tripod head geometry

Doug Kerr

Well-known member
In a recent thread on the Manfrotto 410 three-axis geared tripod head, I mentioned the issue of how the camera is mounted on the head. I though I would discuss a little the theoretical issues involved.

First, a mea culpa. I have often referred to the three angular movements of a tripod head as yaw, pitch, and roll, terms borrowed from marine, aeronautical, and astronautical science.

In fact, those three terms only properly apply to angular movement about three axes that are always mutually perpendicular and are fixed within the frame of reference of the object whose motion is being described (an aircraft, for example).

So from here on, I will use more appropriate notation.

*********

No straightforward mount can provide us with consistent true motion around the yaw, pitch and roll axes. And for us, this is good, since such a repertoire would actually not be generally useful to our photographic needs.

Rather, in typical photographic situations, we want the following "stacking" of movements (we must be concerned with the order of stacking since the axes, unavoidably, will not be always remain mutually perpendicular).

At the lowest level, we typically want movement in the azimuth direction - around a vertical axis (or nearly such).

In the "layer" above that, we want movement in the elevation direction - around a nominally-horizontal axis, in any case perpendicular to the azimuth axis.

In the topmost "layer", we want movement in the roll direction. Here that term is used precisely; its axis is fixed in the frame of reference of the object being moved: the camera. The axis is (ideally) parallel to the lens axis, no matter where the camera is pointed by movement around the other two axes.

We can call this the "roll over elevation over azimuth" configuration.

For typical three-axis geared tripod heads, when the camera is mounted in the suggested way (the camera plate on a Manfrotto 410 has an arrow marked "lens", which is intended to point in the direction the lens aims), that will be the arrangement in effect.

In some cases, we may find that we cannot practically mount the camera in that orientation with regard to the "top layer" of the head, but must mount it at right angles to that orientation.

The result is a geometric arrangement we can describe as having these "movement layers", from top down:

• Pitch (used rigorously) - rotation about an axis running left-to-right across the camera body, parallel to its bottom.
• Rotation about a horizontal axis perpendicular to the pitch axis (roughly "fore-and-aft"). There is no precise technical name I am aware of for this axis.
• Azimuth - rotation about a vertical axis.

What are the implications of this over the "normal" (roll over elevation over azimuth) arrangement? The basic difference can be thought of in terms that arise in the following "thought experiment".

First, we consider the "normal" arrangement.

• We have the camera aimed at a substantial elevation angle (perhaps negative - imagine 60° down).
• The roll (top) movement is at "zero".
• We use the azimuth (bottom) and elevation (top) movements to aim the camera "crosshairs" at the scene point we desire to have at the center of the frame.
• There is a roughly-horizontal line in the scene we would like to run precisely horizontally across the frame.
• We turn the roll (top) movement until that line runs horizontally across the frame.
• The camera crosshairs are still exactly on the target point. (This assumes that the subject is a substantial distance form the camera, so that the displacement between the lens axis and roll axis does not result in significant "translational" image movement.)

Now, we go to the "alternate" configuration.

• As before, we have the camera aimed at a substantial elevation angle (perhaps negative - imagine 60° down).
• The "second" movement is at "zero".
• We use the azimuth (bottom) and pitch (top) movements to aim the camera "crosshairs" at the scene point we desire to have at the center of the frame.
• There is a roughly-horizontal line in the scene we would like to run precisely horizontally across the frame.
• We turn the second movement until that line runs horizontally across the frame.
• Now, the camera crosshairs are no longer exactly on the target point.

Is the latter intolerable? No, we can re-aim the camera. But is it perhaps uncultured - like non-parfocality of a lens. And in any case, it is a difference from the "normal" situation of which we should remain aware.

So if that's the only practical way to mount the camera, why not. But let's not do it otherwise.
 

Asher Kelman

OPF Owner/Editor-in-Chief
The last two examples would benefit from a diagram! and also 2 Asprins!

Now do I gather that the 404 would not keep the cross hairs on the same place in this scenario

Asher
 

Nill Toulme

New member
All of which makes me feel moderately compelled to go back and figure out why I concluded that mounting in the "cultured" direction on the 410 didn't work for me. It may be that I was trying to shoot straight down...

Nill
 

Doug Kerr

Well-known member
Hi, Asher,

The last two examples would benefit from a diagram!
Yes - I was a bit tight for time yesterday. I plan an expanded presentation soon!

and also 2 Asprins!
Of course. Good for many things.

Now do I gather that the 404 would not keep the cross hairs on the same place in this scenario

The presentation applies identically to the Manfrotto 410 and 405 heads (404 owners are on their own). That is:

• If the camera is mounted as described by the head manufacturer, then we have the "ideal" behavior - the aiming point would be held.

• If the camera is mounted at 90° to the orientation described by the head manufacturer, then we have the nikulturniy behavior - the aiming point would not be held.

Like the Pope's socks, embroidered "TGIF" (toe goes in first), the RC4 plate on the Manfrotto 505 (the same one as on the 510) should have an arrow ("lens") showing the aiming direction of the camera when "conventionally" mounted.

Best regards,

Doug
 

Doug Kerr

Well-known member
These photos may help the reader to visualize the difference between "normal" and "rotated" mounting of the camera on a three-axis tripod head.

The head shown is a Manfrotto 410, bearing a Canon EOS 20D body with a Sigma 18-200 mm zoom lens.

I will identify the head movements from the bottom up as A, B, and C. A is in any event the movement we recognize as azimuth (pan).

Example 1

In the first example, "normal" mounting of the camera on the head was used. The roles of the three movements of the head are (listed from top layer down:

C - Roll (camera frame of reference)
B - Elevation ("tilt") (ground frame of reference)
A - Azimuth ("pan") (ground frame of reference)

Initial setup

The initial setup was with C at 0° and B at 0°. The "taking" camera was at essentially the same height as the 20D lens, and the azimuth of the mount was set so the 20D was aimed right at the lens of the taking camera; the taking camera was aimed at the lens of the 20D.

Position 1A

Now, we changed the elevation movement (movement B) to -45° (45° below horizontal), in order to aim at a target on the ground. We see the 20D setup on the left in the set of illustrations below.

Head_axes_F15490R.jpg
Head_axes_F15491R.jpg
Position 1B

Now we changed the roll movement (C) to 15° counterclockwise (as if to rotate the scene in the frame). We see the 20D setup on the right.

We can readily see that the pointing angle of the 20D lens is not affected. The actual location of the axis is moved ("in translation" as the mathematicians say; that is, without change in direction) because the axis of the C movement, while parallel to the lens axis, is not coincident with the lens axis. (Because of the downward tilt of the lens axis, it may appear, because of its "translational" motion, as if its direction changed slightly; it did not. We could have demonstrated this with a shot from overhead, with the taking camera axis perpendicular to the axis of the lens of the 20D; I was in no mood for such acrobatics this morning.)

Example 2

In the second example, "rotated" mounting of the camera on the head was used. The roles of the three movements of the head are (listed from top layer down:

C - Pitch (camera frame of reference)
B - Roll (ground frame of reference) [not a recognized axis]
A - Azimuth ("pan") (ground frame of reference)

Initial setup

The initial setup was with C at 0° and B at 0°. The "taking" camera was at essentially the same height as the 20D lens, and the azimuth of the mount was set so the 20D was aimed right at the lens of the taking camera; the taking camera was aimed at the lens of the 20D.

Position 2A

Now, we changed the pitch movement (movement C) to -45° (45° below horizontal), to aim at a target on the ground. We see the 20D setup on the left in the set of illustrations below.

Head_axes_F15493R.jpg
Head_axes_F15494R.jpg
Position 2B

Now we changed movement B to 15° counterclockwise (as if to rotate the scene in the frame). We see the 20D setup on the right.

We can readily see that the pointing angle of the 20D lens is affected. The aiming point on the scene will now be substantially to the right (from the camera's perspective) of its initial position.

In the next installment we will see actual results on the test camera.

Best regards,

Doug
 

Asher Kelman

OPF Owner/Editor-in-Chief
Doug,

Thanks so much! The pictures really help. Watching a true engineer translate the technical structure and consequence of making adjustments to the geared head is, in itself a fascinating experience. I can see the care you have made to open the right doors in our mind so we can understand.

Appreciated!

Asher
 

Nill Toulme

New member
...We can readily see that the pointing angle of the 20D lens is not affected. The actual location of the axis is moved ("in translation" as the mathematicians say; that is, without change in direction) because the axis of the C movement, while parallel to the lens axis, is not coincident with the lens axis. ...

But that's going to be true whether we have pitch over roll or roll over pitch, is it not, because in either case the axis of rotation is below the center of the lens? One will be more so than the other, but position is off in either case, no? Only a matter of degree?

Nill
 

Doug Kerr

Well-known member
Here, we will see the impact of the two different camera mounting orientations on the actual image.

As before, I will identify the head movements from the bottom up as A, B, and C. A is in any event the movement we recognize as azimuth (pan).

Example 1

Here the camera has been mounted in "normal" orientation on the Manfrotto 410 head.

The roles of the three movements of the head are (listed from top layer down:

C - Roll (camera frame of reference)
B - Elevation ("tilt") (ground frame of reference)
A - Azimuth ("pan") (ground frame of reference)

The tripod was located a little left of the plane containing the "vertical" mullion line in the carpet.

Position 1A

The initial setup was with movement C at 0°, We used the azimuth movement (A) and the elevation movement (B) to aim the camera at the intersection of two "mullion" lines on the pattern of a carpet on the floor. We see the resulting image on the left in the set of illustrations below.

Head_axes_F15497R.jpg
Head_axes_F15498R.jpg

Position 1B

Now we changed the roll movement (C) counterclockwise to angularly align the mullion grid to the frame. We see the resulting image on the right.

Note that there has been only a very small movement of the aiming point (that as a result of the "translational" shift in the lens axis).

Example 2

In the second example, "rotated" mounting of the camera on the head was used. The roles of the three movements of the head are (listed from top layer down:

C - Pitch (camera frame of reference)
B - "Roll" (ground frame of reference) [not a recognized named axis]
A - Azimuth ("pan") (ground frame of reference)

The tripod was in the same location as in example 1: a little left of the plane containing the "vertical" mullion line in the carpet.

Position 2A

The initial setup was with movement B at 0°, We used the azimuth movement (A) and movement C to again aim the camera at the intersection of two "mullion" lines on the pattern of a carpet on the floor. We see the resulting image on the left in the set of illustrations below.

Head_axes_F15499R.jpg
Head_axes_F15500R.jpg

Position 2B

Now we changed the roll movement B to angularly align the mullion grid to the frame (I didn't do a very accurate job - sorry - I was hastening to get to phase 2 of our delicious Sunday breakfast.) We see the resulting image on the right.

We note that the aiming point has been substantially shifted, essentially to the right with respect to the frame.

Best regards,

Doug
 

Doug Kerr

Well-known member
Hi, Nill,

But that's going to be true whether we have pitch over roll or roll over pitch, is it not, because in either case the axis of rotation is below the center of the lens? One will be more so than the other, but position is off in either case, no? Only a matter of degree?

Yes, the shift in aiming point owing to translational shift of the lens axis will be almost the same for either mounting situation.

But what is at issue here is the shift in aiming point caused by the change in the direction of the lens axis when, with "rotated" mounting, the third movement is used to "angularly align" the image. For any substantial distance to the subject, that will be much greater than the change do to translation of the lens axis.

For example, if the subject is a barge moored at the far edge of a canal, shot from the near high embankment wall (say 50' away), and we have to make a 5° rotation of the "roll" movement to align its length with the horizontal axis of the frame, and we use "conventional" mounting, then (for a 20D on a 410 head), the shift in aiming point would be about 0.4" on the barge.

I have to work out the geometry to get the exact number, but, with "rotated" mounting, the shift in aiming point from the needed change in the third movement would probably be on the order of 10-25" on the barge.

(I'll do the math for that next.)

Of course, to eliminate the shift due to translation of the lens axis, we will need a "gimbal" form mount. They are almost invariably (from "top" layer down):

C Roll (camera basis)*
B. Elevation ("tilt")
A. Azimuth ("pan")

* If it has that; often they don't (at least in a suave way), but with some long lenses, when we mount the lens with a foot, that provides the true roll axis.

Best regards,

Doug
 

Doug Kerr

Well-known member
Hi, Asher,
Thanks so much! The pictures really help. Watching a true engineer translate the technical structure and consequence of making adjustments to the geared head is, in itself a fascinating experience. I can see the care you have made to open the right doors in our mind so we can understand.
Thank you so much. That is indeed what I try to do.

Best regards,

Doug
 

Nill Toulme

New member
OK I tried it and you convinced me. It makes a huge difference. Oriented correctly, and especially combined with Live View and the grid overlay, it makes precise alignment very easy indeed.

I think what I may have run afoul of before is that the base of the 410 is considerably smaller than the base of my tripods. The impact of that is that the "pitch" knob comes into contact with the tripod base at an elevation of only about 10 degrees. What I can't remember is what I was doing that called for any more elevation than that.

This is extremely useful and helpful Doug — thanks!

Nill
 

Doug Kerr

Well-known member
Hi, Nill,

Here are the details of the "barge" shot.

The barge is at the far side of a canal. We shoot from the top of a wall on the near side. The horizontal distance from the camera location to the near side of the barge is 50 ft. The edge of the barge deck (along which we will aim) is 20 ft below the camera and horizontal.

The wall on which we have the tripod is inclined laterally at 5° from the horizontal (upward to out left, facing the barge), and we do not adjust the tripod (or use a leveler) to compensate.

Regular mounting

We aim the camera at the target point on the deck edge using movements A (azimuth, in the frame of reference of the top of the wall) and B (elevation, in the frame of reference of the top of the wall).

Then we use movement C (roll, in the camera frame of reference) to "level" the deck edge in the frame. (We move counterclockwise, by nearly 5° - I won't fiddle with the exact amount here.)

The aiming point moves (essentially along the deck edge, on the barge) by about 0.28" to the left (owing to translation of the lens axis from the working of movement C).

"Rotated" mounting (one version)

We aim the camera at the target point on the deck edge using movements A (azimuth, in the frame of reference of the top of the wall) and C (pitch, in the frame of reference of the camera).

Then we use movement B ("roll", in the frame of reference of the top of the wall) to "level" the deck edge in the frame. (We move counterclockwise, by about 5° - again I won't fiddle with the exact amount here.)

The aiming point moves (essentially horizontally) by about 0.39" to the left on the barge owing to the translation of the lens axis from the working of movement B (less than before - the radius is larger than for movement C, as its axis is at a lower layer of the "stack").

And the aiming point moves about 21" to the right on the barge, owing to the change in direction of the lens axis from the working of movement B.

Thus the net movement of the aiming point, essentially along the deck edge, is about 20.6" to the right on the barge.

Neat, wot!

Best regards,

Doug
 

Doug Kerr

Well-known member
Hi, Nill,

OK I tried it and you convinced me. It makes a huge difference. Oriented correctly, and especially combined with Live View and the grid overlay, it makes precise alignment very easy indeed.

I think what I may have run afoul of before is that the base of the 410 is considerably smaller than the base of my tripods. The impact of that is that the "pitch" knob comes into contact with the tripod base at an elevation of only about 10 degrees.

Indeed.

When I put my 410 on my Crown wood tripods (which have very large tops - intended for large view cameras to sit on directly), I have to use a "spacer" to raise the 410 off the "table", else there is not sufficient clearance for the elevation knob for very much elevation (and not much room for my fingers under the azimuth knob either).

The different design of the movements on the 405 (the "elevate" worm is above its gear, not below as in the 410) alleviates the elevate knob problem. (The geometry is the same, just not the physical details.)

image
image
Manfotto 405, seen from "in front, to the left", RC4 plate not quite seated
Manfrotto 410, seen from "behind, to the right"​

Also the 405 has a taller "plinth" under it than the 410, so the "finger clearance under the azimuth knob" problem is alleviated.

So, Asher, tell Wendy that these benefits and the second spirit level alone are worth the extra 180 bucks.

Best regards,

Doug
 

Doug Kerr

Well-known member
Hi, Nill,

Oriented correctly, and especially combined with Live View and the grid overlay, it makes precise alignment very easy indeed.
And remember just a year ago when many "macho" photographers made fun of automatic transmissions on sports cars; no, wait, I meant Live View!

Best regards,

Doug
 

Doug Kerr

Well-known member
Hi, Nill,
And what do you use for a "spacer?"
A 1-1/2" PVC coupling. I use a long 1/4-20 hex bolt up through the tripod table through its center right into the bottom of the 410 (I keep a 1/4 adapter bushing in it to suit the Sunset tripod I mostly use it on).

On the tripod, I put the table insert intended for a 3/8" fixing screw into the table. That way, the shank of the 1/4-20 hex bolt will pass through the insert threads (it is set up for a "captive" fixing screw, and I don't have a lathe anymore to make a long 1/4-20 one).

One project for this weekend is to paint it hammertone black so it doesn't look like a pipe fitting.

I'll send a pic when I get a chance.

Best regards,

Doug
 
Last edited:

Doug Kerr

Well-known member
Here is my Manfrotto 410 mounted, with my "spacer", on a No. 2 Crown tripod, with an EOS 20D on board.

Manfrotto_410_F15504R.jpg

Note that the elevation is still limited to the advertised +30° (as seen in the figure). Above that, the release thumbwheel on the B movement strikes the base of the mount.

Best regards,

Doug
 
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