## 4 Kinematics, Workspace, Singularity, and Simulation
### Actuators, Control, and Safety  
Electrical actuators were selected for the exoskeleton application. Compared to pneumatic actuators, electrical actuators have a substantially larger bandwidth but an inferior power-to-weight ratio. A single actuator that provides a large bandwidth and a high power-to-weight ratio does not exist. An actuator's dynamic response is determined by its bandwidth. A limited-bandwidth actuator reduces system transparency by not being able to deliver the operator high-frequency forces [36]. The Actuonic Motion Devices (Actuonic Motion Devices Inc., Saanichton, BC, Canada) L12-50-210-6-I actuator is the one which was chosen for actuation. Because it is equipped with an internal position controller, the actuator will move to the desired location. It has a 210:1 gear ratio with a total stroke length of 50 mm. Its top speed at no load is 6.5 mm/s, and it can handle up to 80 N of force. It weighs 40 g. The device has a stall current of 460 mA and a maximum input voltage of 7.5 V.  
All three actuators are controlled simultaneously by an Arduino board. The motors are powered by an external battery. The controller is then given inverse kinematic-based trajectory directives. The workspace of the exoskeleton is greater than that of the human arm for specific joint actions (see Table 2). To protect users from these circumstances, hardware stops and software controls are used. Additionally, emergency stop switches are offered. The total cost of setting up the system is less than EUR 390, including the universal joints, actuators, Arduino board, battery, and charger. The control of the proposed exoskeleton is achieved by programming an Arduino board with the inverse kinematic solutions, which moves the human hand using linear electric actuators. In order to follow the desired path, an actuator command must be produced by a control system. The actuator's speed can be adjusted with these commands. No sensors are required to provide feedback regarding the orientation and position of the actuator. For this application, simple position control is sufficient and advanced dynamic control is not required. Finding a control for a dynamical system in the event of an initial disturbance and bringing it to equilibrium as quickly as possible are the goals of optimal control. Since there was no disturbance, optimum control was not applied in this project. Furthermore, our system lacks sensors for feedback, which is a disadvantage of optimal control because some feedback is necessary for optimal control. Additionally, our system is free from uncertainties such as real-time perturbations, therefore a robust control is neither required nor utilized [44]. Since the patients set up and operate the device themselves, the suggested exoskeleton robot uses an open-loop position control to reduce complexity in the design and control strategy. The desired path planning and linear joint movements are controlled by an Arduino control board. The exoskeleton is powered by three linear actuators. The driving link motion has been calculated and interpolated for all points found during the inverse kinematics. After that, an Arduino controller receives the acquired actuator movements and powers the exoskeleton. The motor is moved in each necessary position by the controller using an interpolated step motion. There is a delay before going to the next desired position in order to ensure user safety. The user can immediately stop the device using an emergency switch if it becomes uncomfortable. The electric motor's range is restricted by the Arduino IDE 2.1.1 software, and it is evident that this falls inside the intended stroke length which is at a safe operating range for the given purpose. Furthermore, the modest accelerations and velocities corresponding to human motions guarantee that the device's inertia has a minimal effect on how it functions. The robot'skinematic design was therefore taken into careful account when designing the exoskeleton.