## 2 Requirements of the Robot Patient
### Simulation of STS Movement by Robot Patient  
#### 2.2.1. _Admittance Value of Physical Interaction_  
To use the robot patient to reproduce the STS movement, the physical interaction between the nurse and the patient should be considered. Here, the physical interaction indicates that the speed and direction of the robot patient's movement are dominated by the nurse's supporting force.  
* Magnitude of Nurse's Supporting Force Based on the observations made during STS transfers, it was found that if the nurse exerted a larger force while supporting the patient, the patient was able to stand up more rapidly. In contrast, the patient stood up slowly when a smaller supporting force was applied by the nurse. This observation is also related to kinematics, with respect to the relation between force and acceleration. According to this relation, the magnitude of the nurse's supporting force should proportionally influence the speed of the patient's standing movement.
* Direction of Nurse's Supporting Force The patient's movement generally follows the direction of the supporting force applied by the nurse. For instance, if the nurse exerts a torque to bend the patient's trunk, the patient's hip joint will be flexed. If the nurse exerts a torque to extend the trunk, the patient's trunk will be extended. Accordingly, the direction of the nurse's supporting force was used as a factor in determining the direction of patient movement during STS transfer.  
These observations imply that it is necessary to set the required value of the admittance in the control method of the STS movement. Admittance is the inverse of impedance, and it represents the force-velocity relationship between the external torque (or force) from the environment and the rotational velocity of the joint [41]. First, the external torque was measured from the hip joint, because this joint is close to the waistband that the nurse uses to support the patient. To reproduce the STS movement, the value of the admittance \(Z\) is determined from the following equation.  
\[Z_{joint}=\tau_{external}\ /\ \dot{\theta}_{joint}. \tag{1}\]  
Here, \(\tau_{external}\) represents the external supporting torque; and \(\theta_{joint}\) is the rotational speed of the joint. Therefore, the relationship between the nurse's supporting torque \(\tau_{external}\) and the motion of the patient's lower limb joint (i.e., rotational speed \(\theta_{joint}\)) should be observed in advance. However, as only a few studies have measured both the nurse's supporting torque and the motion of the patient's lower limb joint during STS transfer, the available data are very limited. A preliminary study examined the data obtained from prior work in [5]. According to these results, there is a huge variation in the time required to complete the STS movement with standing assistance, ranging from 4 s to 10 s. Furthermore, we investigated the range of external torques exerted by the nurses. According to clinical experience, lifting a weight greater than 20 kg by a nurse could result in injury, such as lower back pain. Therefore, 20 kg was determined as the maximum torque, and it is recommended that nurses should not exert torque exceeding this value. Further, the nurse usually grips the patient's waistband, which is approximately 40 cm away from the hip joint. Accordingly, the maximum torque that nursing teachers recommend is 39.2 Nm on each hip joint. The quickest possible STS movement was assumed to occur when the nurse adds support with a maximum torque of 39.2 Nm. Therefore, the average rotational speed of the hip and knee joints (from 90\({}^{\circ}\) to 0 \({}^{\circ}\)) is 22.5\({}^{\circ}\)/s, and the corresponding admittance is \(Z\) = 1.74 Nm \(\cdot\) (\({}^{\circ}\)/s)\({}^{-1}\). The value of the admittance \(Z\) can be adjusted when simulating patients with different disabilities. A severe level of disability may correspond to a greater admittance \(Z\) and therefore may require a greater torque to rotate the patient's joint.