*3.2. Calculation of the Blocking Angle*

The proposed morphology is designed with a blocking mechanism that protects or strengthens it at certain angles of inclination and orientation, and that must be parameterized in the kinematics. The angle of inclination at which the blocking occurs depends on the space between the triangular sections, where *Hs* is the height of the point of contact with the bending center of the link, and *Ds* is the distance from the point of contact with the bending center of the link, as shown in Figure 12. However, this distance *Ds* is not a constant parameter as it would be if the sections were circular. The blocking angle depends, in this asymmetric triangular design, on the distance *Ds*, which varies according to the orientation being a maximum value when the point of contact is the vertices of the triangle and a minimum value when the point of contact is the center of the edges of the triangle.

**Figure 12.** (**a**) Diagram showing the link bending with the joint at rest. (**b**) Bending of the beta link at the point where the morphology makes the blocking contact.

From the values *Hs* and *Ds* the angle *α* is obtained as:

$$\kappa = \arctan\left(\frac{H\_s}{D\_s}\right) \tag{10}$$

This angle is formed as the bisector of the blocking angle. The blocking angle of a link, *β*, is given as the double of alpha and it is obtained from the following equation:

$$\beta = 2 \cdot a = 2 \cdot \arctan\left(\frac{H\_s}{D\_s}\right) \tag{11}$$

*Hs* has a fixed value (in our case, 8 mm) while *Ds* varies according to the orientation. To calculate *Ds*, we estimated the maximum, *max*, and minimum, *min*, possible distances with this morphology (40 mm and 25 mm, respectively), and the angles between them, *ψdi f* = 60◦. Knowing the orientation angles where the maximum and minimum occur, it can be parameterized according to a factor such that:

$$\frac{\epsilon\_{\max} - \epsilon\_{\min}}{\psi\_{diff}} = 0.25\tag{12}$$

Based on this factor, we know how the distance between the minimum and the maximum varies for each degree for *Ds*.

Once the theoretical blocking angle, *β*, is estimated for each link according to the orientation, we can calculate the final joint angle, Γ, when blocking occurs.

The final angle depends on the number of links within the joint, *N*, such that:

$$
\Gamma = \beta \cdot N \tag{13}
$$
