# Design and Implementation of a Multi-Function Gripper for Grasping General Objects
## 4 Experimental Evaluation and Discussion
### Discussion  
Two-finger grippers have been extensively used in industrial application and automated assembly because 60 to 70% of human's grasping of objects of cylindrical, parallelepiped, and pyramidal shapes is performed with only two fingers, and two-finger grippers are generally cheaper and easier to use as compared with multi-finger grippers/hands [31; 32]. Our prototype gripper was manufactured using aluminum alloy. Because ball bearings are used at all joints, friction in the joints can be considered to be negligible. Different phases of two-finger grasping with only two contact points are shown in Figure 21. The two fingers will make contact with the object in sequence. From Figure 21b,c, we can see that the object is dragged by the finger during continuous closure movement. Figure 21d demonstrates the phase where a static grasp is achieved. In order to model these phases, the planar grasp model [33] for a two-finger gripper is shown in Figure 22. The static equilibrium condition of a planar grasp can be expressed in the directions of the contact and squeezing line as follows  
\[F_{1}\cos\psi_{1}-F_{2}\cos\psi_{2}+\mu_{1}F_{1}\sin\psi_{1}-\mu_{2}F_{2}\sin \psi_{2}+m_{obj}\Big{(}g\cos\psi_{w}\sin\phi_{w}+a_{y}\Big{)}=0 \tag{8}\]  
\[-F_{1}\sin\psi_{1}-F_{2}\sin\psi_{2}+\mu_{1}F_{1}\cos\psi_{1}+\mu_{2}F_{2}\cos \psi_{2}+m_{obj}\Big{(}g\cos\psi_{w}\cos\phi_{w}+a_{z}\Big{)}=0 \tag{9}\]  
\[r_{\rm A}F_{1}(\sin\psi_{1}-\mu_{1}\cos\psi_{1})-r_{\rm B}F_{2}(\sin\psi_{2}- \mu_{2}\cos\psi_{2})-N-r_{\rm G}m_{obj}\Big{(}g+a_{y}\Big{)}\sin\phi_{w}=0 \tag{10}\]  
where \(F_{1}\) and \(F_{2}\) are the grasping forces at contact points A and B. \(\mu_{1}\) and \(\mu_{2}\) are the friction coefficients at contact points A and B. \(r_{\rm A}\) and \(r_{\rm B}\) represent the distances of contact points A and B. \(r_{\rm G}\) represents the distance of the gravity center. \(W=m_{obj}\delta\) represents the weight vector of the objects. It is orientated with an angle \(\phi_{w}\) with respect to the squeezing line and an angle \(\psi_{w}\) with respect to the perpendicular axis to the y-z plane. \(a_{y}\) and \(a_{z}\) represents the acceleration components of the gravity center point. \(N\) is an external torque acting on the object and the inertia effect due to the manipulator movement is also included. This grasp model describes all situations of a two-finger grasping as pointed out by [PERSON] [34]. Figure 21: Different phases of grasping objects. (**a**) Initial impact. (**b**) Second impact. (**c**) Applying grasping force. (**d**) Static equilibrium. Figure 20: Example of scooping and picking up thin objects lying on a flat surface. From Figures 21 and 22, it can be found that the static equilibrium might be difficult to achieve by using only two grasping forces, especially in the case that the two fingertips are not parallel to each other. From Equations (8) to (10), we can see that with only two grasping forces (two unknowns), it might be difficult to ensure that all those three equations hold. As mentioned earlier, both parallel grasping (two fingertips are parallel to each other) and non-parallel grasping (through adjusting the orientation of the distal phalanx) can be realized by using our two-finger gripper. As far as the parallel grasping is concerned, the parallel grasping force depends on friction forces at the fingertip [35; 36]. The parallel grasping can be achieved by using the outer or interior surface parallelepiped of the fingertip. For cylindrical objects or those with parallel surfaces to both fingers, the parallel or opposed grasping force can be produced. If the directions of these forces coincide and friction forces generated are big enough, the parallel grasping generally can be achieved stably. The friction force depends on the nature of two surfaces in contact. For example, the sliding contact and rolling contact would have different friction forces. And the friction coefficient between the contact surface and the object can be increased by adding a friction pad at the fingertip.