## 3 Materials and Methods
### Apparatus  
The developed haptic system for wheelchair users consists of a robust and sophisticated hardware setup, which can be seen in Figure 1, designed to seamlessly integrate with virtual reality environments, particularly CAVE (Cave Automatic Virtual Environment) systems, which are room-sized virtual reality spaces that project images onto walls, floor, and ceiling to create an immersive experience. The primary objective of this system is to allow wheelchair users to navigate virtual environments using their wheelchairs while providing realistic haptic feedback to enhance the sense of presence and immersion. As users maneuver the wheelchair, the system captures their movements and translates them into the virtual environment (projected in the CAVE) in real time. The system consists of a platform with 4 openings in the floor, corresponding to the places where the wheels of the user's wheelchair should be positioned. In these openings, the two front ones are free rollers, while the two rear ones are rollers where one of each pair is connected to a servomotor. This only happens on the rear wheels because they are usually the driving wheels with which the user interacts (the ones that accelerate or brake). The platform measures 1000 \(\times\) 1000 \(\times\) 150 mm and weighs approximately 75 kg. This compact design ensures that the system can be easily integrated into various VR setups without requiring extensive modifications to the existing infrastructure. The platform features two primary components, the rear and front cylinders, that are critical for the interaction between the wheelchair and the platform, which can be seen in Figure 2, where P refers to the complete platform, R1-R2 and R3-R4 are the cylinders, E1-E3 and E2-E4 are the roller shafts, Z1-Z2 are the support bases for Ex, and Dx refers to the different wheel diameters and Lx to the longitudinal separation between wheels. 1. Rear cylinder: A free-spinning cylinder with a radius of 40 mm, mounted on bearings at both ends. 2. Front cylinder: A driven cylinder with a radius of 80 mm, connected to a servo reducer on one end and a bearing on the other. This cylinder is responsible for generating the required feedback forces. The system is designed such that the driving wheels of the wheelchair fit snugly between the two cylinders. As the user maneuvers the wheelchair, the cylinders rotate, and the system captures the motion data. The core of the haptic feedback system is based on two high-precision servo actuators, which are responsible for both capturing the motion of the wheelchair and providing the necessary haptic feedback. Each actuator is equipped with a servo reducer and an encoder to ensure accurate control and feedback. 1. Servomotor: 1. 1. The servo actuators are controlled via frequency converters, which adjust the motor speed and torque based on the input from the encoders and the simulation software. 1. Specifications: 1. Input Voltage: 1 \(\times\) 200-240 VAC \(\pm\) 10%; 2. Output Voltage: 20-250 VAC (ensure safe and stable operation of the servomotors); 3. Output Frequency: 0-500 Hz. These converters are equipped with integrated network filters (Category C2) to ensure smooth and noise-free operation. The haptic feedback is generated by varying the resistance and assistance provided by the servo actuators, simulating real-world conditions such as inclines and declines. The system's control software adjusts these parameters in real time based on the virtual environment's terrain data and the user's movements. The system communicates with the VR environment via a TCP/IP to SystemBus gateway, ensuring seamless data exchange between the hardware platform and the simulation software. The control software is responsible for managing the communication, processing the encoder data, and adjusting the servo actuator parameters to provide realistic feedback.