Rudder pedals with force feedback
This page describes the rudder pedals with force feedback. The basic force feedback system is described in DIY force feedback interfacing.

There were a number of design considerations for the FF rudder pedals:

bulletRudder pedals need considerable centering force during flight. Some tests showed that forces in the order of 150N (~15kgf) on the pedals would be needed.
bulletTo make sure the centering force is felt at low force settings, the friction in the pedals must be very low. Therefore I opted for full ball bearing pivoting points.  
bullet The pedals still need to have proportional brakes and the mini transducers for wheels and engine vibration transfer.

For the motor coupling to rudder pedals, there needs to be some gearing ratio to obtain sufficient pedal force. The below drawing shows the basic principle: A steel cable wound around a metal shaft will result in shaft rotation when pedals are moved. The shaft diameter will determine the number of rotations over full rudder movement range. The shaft needs to be strongly attached to the frame, as it will take the full rudder pedal force.
A big gear wheel is attached to the shaft. The DC motor with a smaller gear wheel will drive the shaft. 

For the flightsim rudder input, a potmeter is mounted at the rudder bars. The gearing is such that sufficient potmeter rotation (~180 degrees) is obtained.
For the force feedback servo system, a position pickup is placed at the metal shaft gearing, close to the motor drive. This avoids servo instability due to cable slack.  The position pick-up is done with a 10-turn potmeter.

Spec of the (second hand) motor that I used: (Glentek GM2340-15)
Power: 150W, torque: 0.133Nm/A, rated current : 2.5A, DC resistance 2.8 Ohms. Of course you can use other types, but keep in mind that the motor dissipates under stalled conditions, and will heat-up quickly. 

Finding the right gear ratio proved to be quite a challenge: Originally I started the design with a big motor gear ratio for lots of pedal force (~200N) at relatively low motor current. This approach had the following disadvantage: The pedals movement at zero motor current showed considerable friction, due to the fact that the pedal movement resulted in high motor rpm. The DC motor would act as generator, dumping current into the power buffer supply. This resulted in unacceptable rudder pedal friction, especially when quick rudder movements on the runway were needed.
Therefore I experimented with lower gear ratios, finally coming to a compromise between zero drive pedal "friction" and max drive pedal force.  

The total gear ratio's are now as following:
Total pedal movement is 17cm (+/- 8.5cm), total  metal shaft rotation 3.4 turns (shaft diameter = 18mm), shaft gear wheel 60 teeth, motor gear wheel 48 teeth, position pick-up 25 teeth. The motor has a torque constant of 0.133Nm/A. The shaft has 0.133 * 60/48 = 0.166Nm/A torque. The cable wound on the shaft has an 'arm' of 9mm. Since Force = Torque/arm, the force in the cable is 0.166 /0.009 = 18.4N/A. At 6Amps of motor current (62 *2.8 = 100W of motor power)  I get ~ 111N of cable force, about 11.2 kgf. The cables are attached at the outside of the rudder bars (230mm from center), while your feet are slightly inward (190mm from center). This results in ~127N or 13kgf of pedal force to your feet. Calculations and measurement results match pretty well.    

The 10-turn position pick-up potmeter will rotate 8 turns, giving +/- 9.6V from centerpoint when connected to 24V.

The base of the rudder pedals are two metal bars, that hold the pedals. All pivot points have ball bearing.

Completed pedals, including the proportional toe brakes. I added sand-paper for anti-slip.

Toe-brake assembly: I took these out of a junked gamepad. It is mounted such that the pedal pushes the lever.

Detail of the motor to shaft gearing and servo position pick-up.

Video's of the pedals action:
Pedal movement   Gear system   Toe brakes   Servo gain (shows pedal stiffness with increasing servo gain)

Impressions during first system test-flight in Cessna: Everything is working as planned. On runway, the cable system with some motor friction and slight inertia feels pretty real. During take-off, the pedals already become stiffer. In the air, you really need some force to push the pedals. My 13kgf seems a good figure.  "Pushing the ball" now becomes more real, and you're less prone to overdo it like I did in the past. Flying really slow gives you some of that mushy control feeling. Best of all: There is absolutely no delay in the force feedback with this analog servo system.
Next on my list: Adding dynamic force signals to the pedals like a sudden sidewards jolt when touching down with slip.   

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