The problem is that you are using a MEMS digital accelerometer, and what you are reading is the SCK (serial clock) pin of the serial interface. In order to function, that sensor needs to be interfaced with a microcontroller, that sets it for the sampling frequency, the range and so forth.
So you don't have to expect a square wave with 100Hz frequency, but a fast (depending on the bus bitrate) spike, corresponding to a transmission. Expanding the spike, if the scope is fast enough, you should then see the clock square wave inside the spike.
Moreover, if you don't set the SPI interface correctly, the uC will not generate the clock (the sensor operates in slave mode), and you won't read any value.
If you want to see a 100Hz signal, you could probe the Int pin, which sends an interrupt to the microcontroller every time a measure is available. Then, if you handle the interrupt from the microcontroller properly, you wil see the pulse corresponding to the transmission every 10 ms (100Hz).
But make sure that you're not using motion detection; in that case, only when an acceleration is measured, it will generate the interrupt.
To read the data at the SPI port, the simplest thing is to configure the communication with the sensor; otherwise, it won't send data at all. Then, check if the microcontroller is getting the interrupts and if it's reading the data the sensor gives; you can use a timer to add a timestamp to values and check the frequency they come.
(still WIP)
Sadly, this may be a very difficult problem to solve. The problem is that you have almost nothing to use as a reference.
There's no magnetic field, and no suitable gravitational one. So compasses and accelerometers won't help you here. These are the options I can think of:
Gyro: You can measure the rate at which the object is rotating, but not its absolute orientation. By watching the rotation rate all the time, you can estimate your angle by 'dead reckoning' (integration). However, this is really not accurate over long periods of time because the gyro isn't a perfect sensor. More time = more error.
Optics 1: There are a huge number of options here which may be suitable depending on your particular circumstances. Firstly, you could use a camera to look at the inside of the duct. If it's featured enough, you could figure out your angle by looking at the features. If the duct is perfectly smooth on the inside, then perhaps you can shine a laser down the duct to spot on the inside for the prototype to use as a reference.
Optics 2: If the entrance of the duct is still visible from the prototype, then a camera on the prototype could look back up the duct and see the orientation of the outside world to get its bearings.
Acoustics: If you have access to the outside of the duct, then maybe you could repeatedly tap on the outside of the duct, and the prototype could get a sense of direction with a couple of microphones.
How is the prototype being lowered into the duct? On a piece of string? If so, then attach it to a pair of strings instead. That way it won't be able to rotate by itself. You'll do the rotating from the entrance of the duct.
So, basically, all of these options involve some complexity. You won't be able to get a simple analog direction signal from a simple sensor. Almost everything I can think of involves processing power to some degree.
If you can give more details of your problem, we may be able to think of better solutions.
Best Answer
An accelerometer is definitely out in terms of noise.
A mechanical arm system, while potentially accurate enough, may well influence the injection scenario enough to render your results meaningless. I suspect a student struggling to control the position of a small syringe would be distracted by a large measurement arm, no matter how well balanced and low friction.
The only real \$^*\$ options you have are optical.
It should be possible to mark the syringe at both ends of the barrel with fiducial markers. The resolution you can achieve is limited by the optics for pointing multiple cameras at the target. If the test site is small and the location well defined, then you can use zoom optics to make the image fill a significant amount of the frame. HD cameras, and sub-pixel location of the fiducials via something like OpenCV ought to make your target resolution achievable.
\$^*\$ real => low cost, keeps the imaging volume clear, and it's apparent how you'd get the resolution. There are plenty of other modalities, for instance MRI, PET tomography, ultrasound, magnetic tomography, Xray CT, resistive tomography - which need variously calibration, development, expensive equipment etc.