**8. Flexure hinges in the field of robotics**

The combination of flexible fluidic actuators and flexures leads to robotic structures with extraordinary characteristics in terms of weight, compliance, and degree of integration. This

(c) Bending Stiffness of Compliant Structural Element

#### **Figure 28**

28 Will-be-set-by-IN-TECH

with spatial modular kinematics based on FFA modules is considered in [127]. In addition to decentralized SMCTE position controller the active gravity compensation-based on the quasi-static robot model is used in feed-forward loop to take the weight of robot mechanics into account. Experimental investigations, conducted with different loads for soft-robots with 4 and 6 degrees of freedom (DOF), show the behavior, the quality and the limits of the

The application of different control strategies for physical interaction of pneumatic soft-robots with the environment is studied in [147] by simulation and in [9] also by experiment. For control feedback the current measurements of pressure and joint angle position as well as a force/torque observer based on inverted experimental torque characteristics of FFA are used. Hereby the force sensor abilities of FFAs as of a kind of smart actuators are utilized. An adaptive admittance control with trajectory modification (ACTM) is compared by simulation to an adaptive admittance control with variable stiffness regulation (ACSR) using a model of a planar robot with two rotary joints. Both concepts enable desired force tracking in constraint direction and compliant position control in unconstrained direction. Furthermore the more promising ACSR approach was implemented and validated within an experimental set-up using a planar soft-robot with two FFA joint units by tracking even or lightly curved surfaces

Chapter 2.2 showed some examples of how inflatable structures can contribute to compliant robotics. This chapter shows how a modular design can help to integrate inflatable structures in robots independently from the drive concept. The main load cases of robotic structures are bending and torsion. In the shell of inflatable structures we have a state of plane stress. The shell cannot carry significant compressive force. However, when pressurized the shell is pretensioned. Compressive forces thus decrease this pretension in the shell. When the compressive forces overcome the pretension the whole structure deflects and yields the

The general fabrication process of structural elements is identical to the process described in chapter 3.2.1. The different load cases require different reinforcements in the shell. Two different layers are integrated in the shell in order to carry bending and torsion respectively. The fibers of the braided reinforcement follow the directions of the principal stresses for torsion on the surface of a cylinder as shown in figure 28(a). The reinforcement for pressure stability and bending are are shown in figure 28(b). This second reinforcement layer is a woven fabric tube with radial and axial fiber directions. The relationships between internal pressure and bending or torsional stiffness are presented in figure 28(c) and 28(d). These graphs show how the stiffness can be adjusted depending on the compliance requirements. Each front end of the structural element is equipped with a four screw flange, which allows

The combination of flexible fluidic actuators and flexures leads to robotic structures with extraordinary characteristics in terms of weight, compliance, and degree of integration. This

decentralized control concept with and without active gravity compensation.

*6.3.3. Interaction control*

without knowledge of the environment stiffness.

for easy mounting and pressure sensor integration [36].

**8. Flexure hinges in the field of robotics**

**7. Inflatable structural elements**

external loads.

section introduces fiber reinforced flexures fabricated in a VARTM-process (Vacuum Assisted Resin Transfer Molding).

A flexure hinge transforms an applied force into a rotary motion due to its different structural stiffnesses. The shorter the flexure length the more precise is the rotating motion. General consideration of beam theory show how the maximum bending stress *σmax* limits the deflection Δ*x* of the beam [51, 78].

$$
\sigma\_{\text{max}} = \frac{3\Delta x E \frac{h}{2}}{L^2} \tag{11}
$$

Given that the desired deflection cannot be changed, the bending stress can only be influenced by the beam's height *h* and length *L*. By subdividing the bending beam of a flexure hinge the bending stress stays low without losing structural strength (figure 29).

**Figure 29.** Simplified schematic view of a flexure hinge as a subdivided bending beam

Practically this approach is implemented by using woven fiber tapes to reinforce the bending section. The single fiber filaments represent the subdivided beams. After evaluation of technical fibers UHMWPE-fibers (also know under the brand name DYNEEMA®) have been found to meet the requirements best [36].

#### 30 Will-be-set-by-IN-TECH 596 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

Dynamic testing has shown that after 100, 000 cycles, no visible damage is present. Static testing has also been described in earlier work [36]. The properties have found to be extraordinary with operating loads up to 100*N* and a maximum carrying capacity of over 3, 000*N*. The enhanced fabrication process for flexures allows for the production of single-acting (mass 9.1 *g*) and double-acting (mass 11.6 *g*) drives with full integration of the flexible fluidic actuator as well as the position sensor as described in [36]. Figure 30 shows the different joint-modules. These modules now can be freely combined as shown in figure 35.
