MATLAB: Does the angle measured using Transform Sensor block measures only the absolute value of angle, when the actual angle is sinusoidal about zero in SimMechanics R2013b

Question

I am using Transform Sensor block in SimMechanics to measure angle between two rigid bodies. The base and follower frames are in sinusoidal motion relative to each other about Z-axis. However, the measured angle is reporting only rectified output, i.e., negative half sine wave of the signal is multiplied by -1 and reported as positive half wave. The attached model ('SimplePendulum_AngleOnly.slx') shows this behavior with a simple pendulum model.

Answer 1

The output of the 'Transform Sensor' is based on axis–angle representation of rotation in Euclidean space. Please refer to the following documentation in Wikipedia about the axis-angle representation:

https://en.wikipedia.org/wiki/Axis%E2%80%93angle_representation

In essence, any arbitrary rotation in Euclidean space can be represented as two values: a unit vector and a scalar angle. The resultant rotation is obtained by taking the dot product of these two quantities.

Hence, in the 'Transform Sensor', the output 'q' represents only the angle, which is half the information. To get the complete rotation, you can enable the axis output and use the dot product of the two to obtain correct angular rotation between the base and follower. The attached model ('SimplePendulum_AxisAngle.slx') shows the correct output for the simple pendulum model.