*2.3. Prototype*

To choose the soft joint operation, a test platform was designed. The goal is that the rest position of the joint is horizontal. Three motors will be used to operate the joint by tendons, each of which will wind the three tendons (Figure 5).

**Figure 5.** The elements of the platform are the soft joint (**1**), a metal base (**2**), motors (**3**), electronic elements to feed and control the motors (**4**) and other connective elements such as motor supports (**5**), joint bases (**6**) and tendons (**7**).

The fixing base is made up of two 3 mm thick metal plates, to be strong enough to support the test loads. The motors used for the drive are Maxon EC-max 22. The motors are controlled by Technosoft's Intelligent Drives iPOS 4808 MX, which communicate with the PC via busCAN.

Connecting elements have been printed on a 3D printer Creatbot600 pro and Zmorph from PLA (Polylactic acid) material. They are two bases for fastening the soft joint with the metal base, a platform for fastening the electronic elements, three motor fasteners with the metal platform and three winches that are attached to the motor shaft and the tendons,

made of polyester thread, for the activation of the joint. The designed soft joint has been built by 3D printing from NinjaFlex using a Creatbot600 pro printer (Figure 6).

**Figure 6.** (**a**) Motor connected to the winch to wind the tendons for joint actuation. (**b**) Soft joint on the test platform.

#### *2.4. Material Properties and Tests*

One of the most important features when prototyping a soft robotic joint is the choice of material. This design uses NinjaFlex® 3D Printing Filament, a flexible polyurethane material for Fused Deposition Modeling (FDM) printers. This 3D printing manufacturing method and this material were chosen for their ease to use and for allowing variations in percentage or filling patterns of the soft joint body.

The mechanical properties of this material make it a good choice for the purpose of the prototype (Table 1). Its flexibility allows the joint to bend but, at the same time, it is rigid enough to prevent big deformations and resist loads.

**Table 1.** Mechanical properties of NinjaFlex®.


The soft joint design was analyzed in SolidWorks software, which applies a non-linear finite element study on the material. The prototype was modeled as a simple cantilever beam (one of its ends is fixed and a force is applied to its free end). This allows an efficient testing of the design under stresses and strains.

To simplify the simulation, the joint was assumed to be a completely filled solid except for the inner channel, and to simulate the assembly of the real prototype, the soft joint model was assembled including its two support pieces, one at each end.

After the design phase, the prototype was 3D printed using NinjaFlex material with 30% infill. The experiments were performed with this specific prototype.

The model in SolidWorks was tested under different conditions. First, a no-load test was performed on the soft joint, by only simulating gravity and fixing one of the ends, as shown in Figure 7, with the red arrow representing the orientation of the gravity action in the simulation.

**Figure 7.** No-load simulation of soft joint.

One intended use of this soft joint is as a manipulator able to support different loads. Therefore, a second simulation was carried out with a rectangular prism with a fixed mass of 500 gr, homogeneously distributed. This prism represents the weight of the robot gripper in the simulation, Figure 8. In addition, a 10 Newtons downward force is applied to the end effector, simulating an external weight of 1 kg and causing a higher end torque. The simulation shows a deflection of 7.38◦ and a maximum deformation of 0.75 MPa.

**Figure 8.** Simulation of soft joint with a 500 g prism and a 10 N downward force at the free end.

Additionally, another stress study was carried out to check if the yield strength of Ninjaflex is not exceeded. It was noted that when applying 60 N force at the end of the soft joint, as shown in Figure 9, a bending angle of 60◦ was reached and the maximum deformation was 2.9 MPa. Therefore, a no permanent deformation is confirmed when the soft link reaches an inclination angle of 60◦.

**Figure 9.** Simulation of soft joint with a 60 N upward force applied on the free end.

#### **3. Mathematical Model of the Soft Link**

The position of the soft joint is defined as the combination of orientation and inclination, where inclination is the curvature angle of the joint, and orientation is the angle of the plane perpendicular to the base that contains that curvature. It achieves two DOF of flexion from the three tendons, thus the position depends on the distance of the tendons and their combination. Therefore, a mathematical model of the joint has been created to obtain the theoretical distances of the tendons required for a specific position of the end of the joint. This angle is assumed to be zero when it coincides with the Y axis, and the actuators are named counterclockwise as this angle increases, Figure 10a.
