I have a stationary object that spins in place. I want to place an accelerometer on the side of the object to get two metrics:
Instantaneous velocity
Distance travelled since start of spinning
Note: This object spins on only one axis and does not move from its spot
Assuming I can reliably initiate measurements at the time the object starts spinning, are these two metrics achievable?
A gyro, not an accelerometer, is used to measure rotational (angular) velocity. To measure total rotation, integrate the angular velocity with respect to time, after subtracting the stationary offset.
I'm sorry:
The sensor is placed on the side of the rotating object and I want the measurements for the speed that the sensor is traveling through space.
Use your accelerometer to measure centripetal acceleration. The accelerometer readings may be affected by gravity especially if the axis of rotation is not vertical.
Use the distance of the accelerometer from the axis of rotation to derive tangential speed and/or angular velocity.
The accelerometer readings may be affected by gravity
The accelerometer readings will ALWAYS include the acceleration due to gravity.
The sensor is placed on the side of the rotating object and I want the measurements for the speed that the sensor is traveling through space.
An accelerometer cannot be used to measure speed. By integration of accelerometer readings, one can estimate the speed of linear motion, but the estimation rapidly becomes inaccurate. Such linear speed estimation won't work at all on a rotating object.
jremington:
The accelerometer readings will ALWAYS include the acceleration due to gravity.
NO. It would only be necessary to read one axis of the accelerometer. If that axis is always horizontal, the reading will not be affected by gravity.
jremington:
An accelerometer cannot be used to measure speed. By integration of accelerometer readings, one can estimate the speed of linear motion, but the estimation rapidly becomes inaccurate. Such linear speed estimation won't work at all on a rotating object.
The original post states that the object is stationary (but spinning).
Use your accelerometer to measure centripetal acceleration. The accelerometer readings may be affected by gravity especially if the axis of rotation is not vertical.
The accelerometer will be placed on the object that is stationery and rotating. The accelerometer itself will never be rotated in place, and therefore, upon initiation, I can set offset calibration values to negate gravity acceleration values.
Will this work? An estimation will be good enough, I am sure.
Yes, my office stationery is rotating at approximately one revolution per 24 hours. Most people would call that stationary stationery.
What is the plane of rotation relative to gravity? Something that is constrained to only spin horizontally will be much easier to measure than any vertical component.
An accelerometer rotating about a fixed axis of rotation is going to see two effects. One is a centripetal force proportional to the speed rotation and it's radial distance from the axis of rotation. The other is the effect of gravity as the orientation of the accelerometer changes from the rotation.
Consider two degenerate configurations:
The axis is vertical and the accelerometer is oriented to sense radial acceleration. Since gravity is orthogonal to the accelerometer the rotational speed is directly proportional the sensed acceleration. If the force is significantly above the noise floor of the accelerometer this could work pretty well to gauge speed of rotation. It won't be able to determine the current position of the rotating object and it probably won't work well for a slowly rotating object.
The axis is horizontal with the accelerometer orientation. In this case the sensor sees 1 G when it pointing down, -1 G when pointed up, and 0 G when directly in between. Ignoring centripetal forces it will see COS(angle) where 0 degrees is "pointing" down. With this system it would be straightforward to measure both speed of rotation and orientation, but there is ambiguity in which direction the object is rotating. That could be resolved by using a two axis accelerometer.
Extending this, one could solve the problem with arbitrary axis of rotation with a three axis accelerometer, but the math gets considerably harder. Off hand, the most limiting application is a slowly rotating object on a vertical axis where centripetal force is small and gravity is along the axis of rotation. Unfortunately, I gather that this is the case for the original poster.
MrMark:
Consider two degenerate configurations:
1.The axis is vertical and the accelerometer is oriented to sense radial acceleration. Since gravity is orthogonal to the accelerometer the rotational speed is directly proportional the sensed acceleration. If the force is significantly above the noise floor of the accelerometer this could work pretty well to gauge speed of rotation. It won't be able to determine the current position of the rotating object and it probably won't work well for a slowly rotating object.
2.The axis is horizontal with the accelerometer orientation. In this case the sensor sees 1 G when it pointing down, -1 G when pointed up, and 0 G when directly in between. Ignoring centripetal forces it will see COS(angle) where 0 degrees is "pointing" down. With this system it would be straightforward to measure both speed of rotation and orientation, but there is ambiguity in which direction the object is rotating. That could be resolved by using a two axis accelerometer.
The No.1 is pretty close to but No.2 I try it before.
If the speed is slow it can but Speed up to 40KM or more...I sure the Speed over 50KM then 0 degrees is very hard to get it.
and my project still try to find which way is better so......I go back to work.
Vincent