## 3 Experiments  
### Adjustable Balancing Mechanism Design  
The kinematic and dynamic parameters of the stackable arm are given in Appendix A. The payload corresponding to the mass of a drill attached at the distal end is also given for both the counterweight and spring balancing. In the counterweight based balancing approach, the counterweights \(m_{c1}\) and \(m_{c2}\) were calculated as 2.331 kg and 139 g, respectively, according to Equations (11) and (12). In the design of the adjustable balancing mechanism, we set the maximally allowed extended link length (\(L_{c1}\) and \(L_{c2}\) in Figure 4a) of the counterweight to be 50 mm. Then, considering the relationship between the counterweight and variable payload, the maximum variation of the payload was calculated as 34.75 g. This is too small compared to the nominal mass (1.28 kg) of the drill. In the spring-based balancing approach, the stiffness of the spring was calculated as 1.351 N/mm and 1.0632 N/mm, according to Equations (18) and (19), respectively. It is, however, noted that the spring \(k_{2}\) is not appropriate adjustable balancing since the insertion of this spring on the link \(l_{5}\) is too limited, as shown in Figure 4b, because of its short link length. Thus, using only two springs for adjustable balancing is not appropriate. Therefore, another adjustable balancing approach that combines both counterweights and springs is considered in this study. In fact, there are several possible combinations. From the mechanical point of view, controlling the attachment position of the spring is too difficult to realize. Therefore, we recommend that the spring should be used for supporting a large weight and that the counterweight should be used for taking care of the precise adjustable balancing. However, using two springs and two counterweights causes the system to be too complex. Thus, we adopted an approach that employs one spring and two counterweights. The role of one spring (namely, \(k_{1}\)) is to replace a heavy counterweight \(m_{c1}\). By setting the mass of the two counterweights to be as small as possible, we can minimize the entire inertia of the system and can also cope with payload variation by adjusting the extended link length. In this case, Equation (28) is modified as follows:  
\[\left\{ \begin{array}{l}\overrightarrow{g}\circ C_{1}\overrightarrow{l}_{1}+k_{1} \overrightarrow{S}_{11}\circ\overrightarrow{S}_{12}=0\\ \overrightarrow{g}\circ C_{2}\overrightarrow{l}_{5}=0\end{array} \right., \left\{ \begin{array}{l}\alpha-m_{c1}\frac{L_{c1}}{l_{1}}=0\\ -\alpha\frac{l_{2}}{l_{5}}+m_{c2}\frac{L_{c2}}{l_{5}}=0\end{array} \right. \tag{29}\]  
where by initially setting one counterweight (namely, \(m_{c1}\)) as a small value, the stiffness \(k_{1}\) can be determined from \(\overrightarrow{g}\circ C_{1}\overrightarrow{l}_{1}+k_{1}\overrightarrow{S}_{1 1}\circ\overrightarrow{S}_{12}=0\). Then, the other counterweight (namely, \(m_{c2}\)) is obtained from \(C_{2}=0\), since it is the condition of \(\overrightarrow{g}\circ C_{2}\overrightarrow{l}_{5}=0\). Finally, we only need to control \(L_{c1}\) and \(L_{c2}\) to perform adjustable balancing associated with a variation of payload (\(\alpha\)). In the design process of the adjustable balancing mechanism, two counterweights were calculated as \(m_{c1}=488\) g and \(m_{c2}=910\) g for the given link length of \(l_{1}~{}=~{}l_{3}~{}=~{}200\) mm. The maximum variable-range of \(L_{c1}\) and \(L_{c2}\) was set as \(50\) mm, and the range of the added payload was set as a quarter of \(m_{c1}\). We applied the balancing arm to a surgical ear operation. This device shown in Figure 5 has 5-DOF, including a rotating module with 2-DOF mounted on the 3-DOF translational stackable mechanism. At the very distal end a drill is attached, but it is often replaced during the operation. Therefore, a variable payload occurs during the operation. In the first design, only the two counterweights are used. In the second design, one spring and two counterweights are used for gravity compensation.