**4. Kinematics of finger modules**

The kinematics of this hand is complicated, because all links are subordinated by 1 D.O.F and the motion is driven by linear and rotary movement. All parameters for kinematics are shown in Fig. 11 and parameters are described in Table. 2. The most important part in kinematics is to know <sup>1</sup> from input from screw-nut (,) *Ux y d d* . Because this hand has only 1 D.O.F, the angle which is controlled is only<sup>1</sup> . The left angles, <sup>2</sup> ,<sup>3</sup> are decided by 1 through kinematics. The purpose of this hand is not grasping but gesture, so the fully bended angles are decided to make fist shape. From this, the initial angles are 123 0, 0, 0 and final angels are 123 60 , 90 , 45 *ooo* when maximum distance of nut is 6mm and these angles are used as the boundary condition to solve equations. The length of each phalange is already determined from original human hand and the length of inner links is design factor. From boundary condition and simple model by CAD, the length of inner links can be earned without kinematics. The kinematics was used to check these approximate values and the relations between angles. The geometric method was used to solve and the Matlab was used to organize and solve equations.

The equation of 1 from input (,) *Ux y d d* is given as follows formula (1) by geometric method. The const. is 6mm from design and the angle of *P*1 is <sup>120</sup>*<sup>o</sup>* . When it is used to hardware, the formula (1) is used only, because 1 2 , are not needed to control and full kinematics is complicated and this can calculate slowly by computer. To know 2 , the position of *P*<sup>3</sup> should be calculated and the length of 2 4 *J P* which is the distance between the center of rotation of middle phalange 2*J* and *P*<sup>4</sup> . From these factors, the 2 can be solved in formula (2).

92 The Future of Humanoid Robots – Research and Applications

hand which has the closest shape to human can be produced. Fig. 10 shows the mock-up,

The kinematics of this hand is complicated, because all links are subordinated by 1 D.O.F and the motion is driven by linear and rotary movement. All parameters for kinematics are shown in Fig. 11 and parameters are described in Table. 2. The most important part in

through kinematics. The purpose of this hand is not grasping but gesture, so the fully bended angles are decided to make fist shape. From this, the initial angles are

of nut is 6mm and these angles are used as the boundary condition to solve equations. The length of each phalange is already determined from original human hand and the length of inner links is design factor. From boundary condition and simple model by CAD, the length of inner links can be earned without kinematics. The kinematics was used to check these approximate values and the relations between angles. The geometric method was used to

method. The const. is 6mm from design and the angle of *P*1 is <sup>120</sup>*<sup>o</sup>* . When it is used to

position of *P*<sup>3</sup> should be calculated and the length of 2 4 *J P* which is the distance between the

kinematics is complicated and this can calculate slowly by computer. To know

center of rotation of middle phalange 2*J* and *P*<sup>4</sup> . From these factors, the

 , 

and final angels are 123 60 , 90 , 45 *ooo*

solve and the Matlab was used to organize and solve equations.

hardware, the formula (1) is used only, because 1 2

<sup>1</sup> from input from screw-nut (,) *Ux y d d* . Because this hand has only 1

 <sup>2</sup> ,

when maximum distance

are not needed to control and full

2 , the

2 can be solved in

<sup>3</sup> are decided by

1

<sup>1</sup> . The left angles,

1 from input (,) *Ux y d d* is given as follows formula (1) by geometric

mold and the artificial skin.

Fig. 10. The mock-up, mold and finished artificial hand skin

**4. Kinematics of finger modules** 

D.O.F, the angle which is controlled is only

kinematics is to know

123

The equation of

formula (2).

 0, 0, 0 

 

Fig. 11. The simplified image of finger and parameters


Table 2. Parameters for kinematics.

$$\begin{aligned} \theta\_1 &= \cos^{-1}(\frac{u\_1}{\sqrt{{x\_d}^2 + {y\_d}^2}}) + \sin(\frac{y\_d}{\sqrt{{x\_d}^2 + {y\_d}^2}}) - \theta\_{11} \\ &\text{where} \\ u\_1 &= \frac{{x\_d}^2 + {y\_d}^2 + {r\_1}^2 - l\_4^{-2}}{2r\_1}, \ (x\_d, y\_d) = \mathsf{U}(x, y) \end{aligned} \tag{1}$$

$$\theta\_2 = \cos^{-1}(\frac{r\_2^2 + \overline{I\_2 P\_4}^2 - \overline{P\_3 P\_4}^2}{2r\_2 \cdot \overline{I\_2 P\_4}}) - \theta\_{21} \text{ ( $\theta\_{21}$  is from design)}\tag{2}$$

The formula (2) needs *P P*3 4 and this can be known formula (3) which are the relations between *P*2 and *P*<sup>3</sup> , because the *P*4 can be earned from 2 4 *J P* .

1

Design of 5 D.O.F Robot Hand with an Artificial Skin for an Android Robot 95

In this paper, 5 D.O.F hand for an android robot with an artificial skin was presented. The hand of an android robot required human like appearance because of an android robot is the nearest robot to human. The presented robotic hand has 5 D.O.F fingers and its shape and size are based on Korean young woman. There are three design policies which are size, shape and skin to make this hand and these are for the closest realization of human hand. The finger used D.C motor, screw-nut and liner potentiometer and linkage structure as a power transmission. The characteristic of mechanical design is a modular structure. Each finger module has its own power and sensor independently, so this design can bring easy maintenance by changing modules. The finger module was designed to suit the shape which is based on 3D data from human hand. The hand is just combination of each finger module and palm part. The palm part decides the shape of hand by arrangement of finger modules and it is also designed by 3D data based on human hand. The artificial skin was made of silicon complex which was selected as the nearest material to human skin. To make this silicon complex, mock-up and mold and mixture of materials are needed. After these processes, the closest android hand to real human hand can be produced. This hand is not for grasping but gesture, so experiments are for evaluation how it has similar appearance to human hand and can make variable gestures. In experiments, this hand can express variable postures include rock-paper-scissors and its appearance is similar to human hand. There are some improvements to this hand. The 5 D.O.F is not enough to realize variable gestures of human hand especially spread of fingers and adduction-abduction. In addition, the exact valuation standard of similarity in appearance should be researched. These should be the

Fig. 12. The 6 postures with completed hand.

**6. Conclusion** 

future works in this research.

$$\begin{cases} l\_6 = \sqrt{\left(P\_{3x} - P\_{2x}\right)^2 + \left(P\_{3y} - P\_{2y}\right)^2} \\ P\_3 = f(l\_2) \end{cases} \tag{3}$$

The 6*l* is the designed value and *P*3 can be known by forward kinematics from <sup>2</sup>*J* . These formulas are also solved by Matlab, because they are too complicated to solve by hand. The structure of distal joint is simple 4 bar linkage, so the 3 can be solved easier than1 , <sup>2</sup> . The 3 is known by solving simultaneous equations (4).

$$\begin{cases} l\_7 = \sqrt{\left(P\_{4x} - P\_{3x}\right)^2 + \left(P\_{4y} - P\_{3y}\right)^2} \\ P\_5 = f(l\_3) \end{cases} \tag{4}$$

How to get unknown values is same to get unknown in <sup>2</sup> .

Even if the complicated kinematics was solved, it was not used to operate hand except for calculating 1 .
