# Homework Help: Detecting jumps on a trampoline

Tags:
1. Nov 9, 2015

### Ghostava

I'm an mobile developer. I'm developing system that detects and counts jumps on a trampoline. I will describe in few words the architecture of system.

The system consists of a trampoline, three-axis accelerometer attached to the bottom of the trampoline and a smartphone. All communication (sending acceleration data) take place via bluetooth.

What I know: the mass of the person that will be jumping, and the distance from the surface on which trampoline stands to the trampoline mat.

And here is my question. How to design an algorithm to detect and count jumps. Should I use digital signal processing? Statistic methods? Should I consider analyzing energy transfer between potential, kinetic, spring energy?

2. Nov 9, 2015

### Nidum

Do you mean how many times person jumps from mat onto trampoline or how many jumps person does when already on the trampoline ?

3. Nov 9, 2015

4. Nov 9, 2015

### BvU

Hello Spooky, welcome to PF !
You could idealize the system a bit to have a start: no x, y accelerations, only z. So a standing spring that gets compressed and rebounds. There will be some noise at the point the jumper leaves the trampoline again. Perhaps a low-pass filter and a discriminator are already enough for the counting purpose you mention.

5. Nov 9, 2015

### Staff: Mentor

What do the signals you're getting out of the accelerometer look like?

6. Nov 9, 2015

7. Nov 9, 2015

### BvU

We did a bungee jump thread a year ago. It's somewhat the same set of equations. I kept the simulator file; here's a picture:

Jumper m = 100 kg, starts at 0 m with 0 m/s ; chord is 20 m long and has k = 100 N/m

Top: acceleration of the jumper due to the chord (he also experiences a constant -9.81 m/s2 from gravity). Chord is taut after 2 sec.
Mid: speed in vertical direction. So after 2+ sec (when a_bungee > g) speed is at a minimum.
Bot: vertical position. Sine wave for x < -20, parabola for x > -20.

Your accelerometer gets a huge shock when the jumper hits the mat, so at t = 2 sec you get a huge negative peak, hopefully short, but probably with some nasty spikes (hence my low-pass idea). Then it follows the positive sinusoid and when the jumper leaves the mat you get another negative peak and some oscillations.

Your spring constant from the mat is far more important than the distance from the mat to the floor.
Second important factor is the damping of the mat.

Nice project ! Keep us posted, I especially look forward to seeing what signal you get !

--

8. Nov 9, 2015

### BvU

There's no beating Google; in this case something of a spoilsport. I do notice these links often talk about image analysis, "motion" sensors etc. And the latter often are attached to the sporter.

Still would like to peek at the signals Spooky gets. Do you have maxon Epos or some other software to process the signal ? (see also this thread)

9. Nov 9, 2015

### Nidum

Pun intended of course (!)

Shouldn't be difficult to detect the basic jumping cycle but it may be much more difficult to distinguish true jumps where athlete leaves the trampoline surface by a significant distance from simple bounces where athlete leaves trampoline surface by very little or not at all .

10. Nov 9, 2015

### BvU

Of course! Having fun on PF is more fun with a spuntaneous pun !

11. Nov 10, 2015

### Ghostava

Thanks for all your responses. Let me give you some more details.

The procject is based on Arduino platfrom and it consists of two part: the microcontroler with bluetooth and connected to it by cable circuit board with the 3-axis accelerometer. When the system is turned on the accelerometer automatically starts measuring the acceleration. When I connected to the system via bluetooth automatically sends data. The sampling frequecy of accelerometer can be set from 0.05 Hz, 0.10 Hz, 0.20 Hz, 0.39 Hz, 1.56 Hz, 3.13 Hz, 6.25 Hz, 12.5 Hz, 25 hz, 50 Hz, 100 Hz, 200 Hz, 400 Hz, 800 Hz up to 1600Hz. The data of from the accelemeter is collected in the main loop that is executed by microcontroller and put with the delay of 20 ms on serial port where the bluetooth module is connected.

I do not know nothing about the spring constant and damping of the mat. Why should care about it ? Is there an easy way to calculate it?
I attach the chart of acceleration on z axis of 10 jumps.

I also attach two cvs files with the measurements.

#### Attached Files:

File size:
13 KB
Views:
34
• ###### 10Jumps400Hz.cvs.txt
File size:
31 KB
Views:
39
12. Nov 10, 2015

### BvU

Wow! Will look.

13. Nov 10, 2015

### rcgldr

One issue is that the trampoline surface will oscillate after the trampolinist leaves the surface of the trampoline. The safety mats around the edges of a trampoline may also bounce on and off the springs, depending on how they are located, so high frequency small movments should be ignored. The trampolinist is also exerting downwards force with muscles in addition to the downward force related to upwards acceleration (or upwards deceleration) times mass during a bounce. On a side note, the terminology used by trampolinists is "bounce", not "jump".

14. Nov 10, 2015

### BvU

Quite a bit to say about this ! I think the 6.25 Hz isn't very useful: the signal saturates at both ends -- why at different levels at the positive side is somewhat mystical to me. The -20 V is from some supply voltage I would guess.

The 400 Hz looks much more promising, but also saturates at the - 20 V level. Something that should be fixed before any sensible signal processing can be done.

I subtracted the average ( whole 1035 points sequence - 9.229, quiet period 200 - 400 : -9.77, I fiddled and added 9.729) and 'integrated' to get speed (top picture). Not spot on, quiet period should give 0.

And the horizontal sections while the 'bouncing' is in progress aren't at the zero level at all -- a sure sign that the saturation at - 20 V is a real nuisance because it builds up. But they are nicely distinguishable, so that's encouraging. At the end of a quasi horizontal section, the speed goes up first, then down. Doesn't look like post 7 (the 'up strokes' -- when the acceleration of the 'bouncer' in post 7 is > 0) at all. A sign problem ?

I tried to correct a little (red line is linest fit from 515 to 1035) and then integrate to get 'x' , but you can see how the offsets/drift spoil the picture.
Still, the parabola-like shapes (albeit upside-down !?) are clearly present.

First thing to do: get rid of the saturation. A voltage divider between sensor and detector should do the trick (if the input range can't be adjusted otherwise). Then try a similar signal analysis again.

"Why should care about it ?" Gives you a start if you need to do some frequency filtering. And a little understanding never hurts ...

15. Nov 15, 2015

### BvU

So how's our bouncer doing ?