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I found on SparkFun a module which detects movement in 9 degrees of freedom (DOF). I'm only aware of 6 DOF: translation in X, Y, Z direction, and rotation about X, Y and Z axis. What are the other three?

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I'm aware that there are robots with more than 6 DOF, but in these each segment has only 6 DOF maximum. The human hand (including wrist) has 23 DOF.

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    \$\begingroup\$ please do not use a signature. \$\endgroup\$
    – Kortuk
    Commented Nov 30, 2010 at 17:21
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    \$\begingroup\$ @Stevenvh, I was just letting you know because I have edited it out many times. Signatures are not allowed, but I understand your want to do them. \$\endgroup\$
    – Kortuk
    Commented Nov 30, 2010 at 19:18
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    \$\begingroup\$ @Ralph, I am sorry if you feel otherwise, SO had a very large discussion, if you have a question with 4 answers and everyone adds a little signature then you greatly increase the length of the page. And what does the signature add? I am the rule enforcer, I am sorry if you do not like them. Every post is signed by the user with his name and ID. On your profile you can post information related to your specific background. By signing, you are doubling the space this takes per page. I would love to discuss this in chat if you still have concerns. \$\endgroup\$
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    \$\begingroup\$ @Stevenvh, I am trying to be polite, in general you will notice I do not remove someone saying, "Hope this helps". It is not worth it. However, removing signatures is not a matter that is up for discussion, it is a hard rule that existed before I started moderating and one that had a large amount of discussion before a decision was met. \$\endgroup\$
    – Kortuk
    Commented Dec 2, 2010 at 20:24
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5 Answers 5

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I think that the other three with that module are the outputs from the magnetometer.

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  • \$\begingroup\$ Yes, that was my idea as well, but they're not DOF; you can have a change in the magnetometer's reading unless you move in at least one of the other DOF. Unless your magnetic field moves with respect to your reference system. But then they're not real DOF. Otherwise you could add a light sensor and call it a 10th DOF. It isn't. You may call it a parameter though. \$\endgroup\$
    – stevenvh
    Commented Nov 30, 2010 at 17:21
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    \$\begingroup\$ The Sparkfun sensor has a "fake" extra three degrees of freedom with the magnetometer. If you were using the input from the IMU in a Kalman filter or state-space representation, you would have 9 sources of data, but only 6 possible mechanical directions of motion. The additional data sources may provide you with a more accurate idea of how you have moved, though. \$\endgroup\$
    – mjcarroll
    Commented Nov 30, 2010 at 17:52
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    \$\begingroup\$ @mjc: Specifically, the long-term integral error of the magnetic sensor (compass) is effectively nil, which can be used to eliminate that error from the gyroscope. \$\endgroup\$
    – Nick T
    Commented Nov 30, 2010 at 19:10
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    \$\begingroup\$ As an additional note, you may find that actually measuring more degrees of freedom can be a detriment in some controls applications. This is especially true with cheaper sensors and high-noise environments. If you only need to control one degree of freedom, then the added noise from the other 5-8 measurements may make the control more difficult. \$\endgroup\$
    – mjcarroll
    Commented Nov 30, 2010 at 20:26
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As I read the description I guess they just added the signals that are measured: 3 gyros (orientation) + 3 accelerometers + 3 magnetic field sensors = 9. Makes no sense to me, the gyros and magnetic field sensors essentially measure the same thing (orientation), although I think gyro's are more usefull for small changes, and magnetic field sensors are better for long term stability, so they complement each other.

But adding it all up to 9 is sales speak in my book. They might as well add a temperature sensor and call it a 10 DOF board.

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  • \$\begingroup\$ Also add a stopwatch to call it a 11 DOF board. \$\endgroup\$
    – Efreeto
    Commented May 23, 2019 at 7:10
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That's odd to include magnetic sensors as degrees of freedom; those are dependent variables whereas I expect if I have 9 d.o.f. (degrees of freedom) then I have 9 servos I can control, with orthogonality. I expect a linear basis in common; if someone says saw suction counted, I'd have to call that bogus, though it could easily occupy the same control loop hardware.

Anything further merely defines those servos; whether it's rotary, angular, extension, grip pressure, grossly limited or not, etc. just clarify what's been constructed on the 9 axes available. There's no reason to expect x,y,z and the first and second derivatives of them; or simply the fist derivatives and rho/theta/phi angle, would have any cardinality without the descriptive data necessary to form the Hermetian of those variables.

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You can get 9 DoF if you consider the angular velocities as separate to the instantaneous orientation. 6 DoF will just give you an absolute static position and orientation. There is a extra 3 DoF for the acceleration and a DoF for angular velocities. This actually makes twelve in all, but we don't have an absolute (or relative) position so we loose 3 DoF.

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Calling them degrees of freedom is market speech, but it makes some sense.

When you speak of degrees of freedom of an rigid body, you mean the independent parameters that define its position and orientation in space.

When you speak about sensors, you have accelerometers, which give you the second derivative of position in space, so not really degrees of freedom, but still independent. Gyroscopes, first derivative of orientation, again not degrees of freedom but independent. Together, under given assumptions they allow you to compute the six degrees of freedom.

Then came the market speech: boxes sold which included the six sensors, then boxes came along including magnetometers, so six became nine. Maybe tomorrow we will add barometer to get to 10?

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  • \$\begingroup\$ Note this question is from 2010, so you might get no response from the OP. \$\endgroup\$
    – P2000
    Commented Jun 24, 2020 at 17:20

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