*3.5. Direct Kinematics*

A direct kinematics is also provided through the works collected in [3]. This kinematics allows us to know the inclination and orientation for the input values *L*1, *L*<sup>2</sup> and *L*3. These equations assume that the curvature is constant throughout the flexible body.

$$\psi = \arctan\left(\frac{\sqrt{3}(l\_2 + l\_3 - 2l\_1)}{3(l\_2 - l\_3)}\right) \tag{14}$$

$$\theta = \frac{2\sqrt{l\_1^2 + l\_2^2 + l\_3^2 - l\_2l\_1 - l\_2l\_3 - l\_1l\_3}}{a(l\_1 + l\_2 + l\_3)}\tag{15}$$
