Figure 1.
CAD model of the ExoReha upper extremity exoskeleton
Figure 2.
ExoReha kinematics model
Figure 3.
Initial open bearing design
Figure 4.
Exoskeleton multibody model for dynamics analysis
Table 1.
Mass parameters of the multibody model bodies (Iqq – main inertia moment along q axis)
| Body | Mass | Ixx | Iyy | Izz |
|---|---|---|---|---|
| [kg] | [kg · mm2] | [kg · mm2] | [kg · mm2] | |
| 1 | 0.9 | 1013.4 | 918.0 | 1369.0 |
| 2 | 1.3 | 6705.0 | 5734.0 | 2448.2 |
| 3 | 1.1 | 6553.9 | 6196.3 | 2614.4 |
| 4 | 2.0 | 10605.0 | 38714.7 | 37689.3 |
| 5 | 1.2 | 7627.1 | 3805.2 | 8066.9 |
| 6 | 1.6 | 11756.7 | 23986.1 | 25468.9 |
| R1 | 3.0 | 413000.0 | 1861000.0 | 2011000.0 |
| R2 | 2.5 | 345000.0 | 1504809.0 | 1312510.0 |
Table 2.
Coordinates of COMs (centers of masses) of the elements in the local coordinate systems (COMq – center of mass along q axis)
| Body | COMx | COMy | COMz |
|---|---|---|---|
| [mm] | [mm] | [mm] | |
| 1 | 1013.4 | 918.0 | 1369.0 |
| 2 | 6705.0 | 5734.0 | 2448.2 |
| 3 | 6553.9 | 6196.3 | 2614.4 |
| 4 | 10605.0 | 38714.7 | 37689.3 |
| 5 | 7627.1 | 3805.2 | 8066.9 |
| 6 | 11756.7 | 23986.1 | 25468.9 |
| R1 | 413000.0 | 1861000.0 | 2011000.0 |
| R2 | 345000.0 | 1504809.0 | 1312510.0 |
Table 3.
Maximum angular velocities which may occur in DOFs
| DOF | ωmax [rpm] |
|---|---|
| φ1 | 23.33 |
| φ2 | 21.67 |
| φ3 | 21.67 |
| φ4 | 23.33 |
| φ5 | 13.33 |
Figure 5.
Analyzed bearing configurations; from left: -90 deg, 0 deg, and 90 deg
Figure 6.
The outer part geometry prepared in the SpaceClaim
Figure 7.
The inner part geometry prepared in the SpaceClaim
Table 4.
Parameters of finite elements models
| Element | No. of elements | No. of nodes |
|---|---|---|
| Inner part | 161,215 | 240,101 |
| Outer part | 108,993 | 171,687 |
Figure 8.
Constraints of the outer part
Figure 9.
Constraints of the inner part
Table 5.
Material properties for FEM analysis
| Material | Iglidur I190-PF | F3D NanoCarbon (PA12 + CF) |
|---|---|---|
| E [GPa] | 1.66 | 6.02 |
| v | 0.306 | 0.306 |
| Yield strength [MPa] | 27.25 | 98.79 |
| Tensile strength [MPa] | 36.06 | 130.73 |
Figure 10.
Optimization parameters set
Table 6.
FEM model parameters initial values (input parameters: P1-P5 and Material model, output parameters: maximum stresses and masses of the parts)
| P1 [mm] | 15.0 |
| P2 [mm] | 20.0 |
| P3 [mm] | 30.0 |
| P4 [mm] | 60.0 |
| P5 [mm] | 50.0 |
| Material model | Iglidur I190-PF |
| Max stress in inner part [MPa] | 12.68 |
| Max stress in outer part [MPa] | 9.49 |
| Inner part mass [kg] | 0.96 |
| Outer part mass [kg] | 0.85 |
Table 7.
Considered ranges or discrete values of FEM model parameters
| P1 [mm] | 10 – 16 |
| P2 [mm] | 15 – 20 |
| P3 [mm] | 26 – 30 |
| P4 [mm] | 48 – 60 |
| P5 [mm] | 40 – 50 |
| Material model | Iglidur I190-PF/F3D NanoCarbon |
Table 8.
Equivalent load states for the considered combinations of bearing arrangements (DOF column represents the DOF for which the parameters are presented with the configuration in the open bearing by the rotation in degrees, Fq – force along q axis of the global coordinate system, Mq – force along q axis of the global coordinate system)
| Case | DOF | My [Nm] | Mz [Nm] | Fx [N] | Fy [N] | Fz [N] |
|---|---|---|---|---|---|---|
| 1 | φ3 = —90° | -22.91 | 42.41 | -411.78 | 14.00 | 0.67 |
| φ5 = —90° | -2.82 | -29.45 | -96.72 | 184.97 | 50.72 | |
| 2 | φ3 = —90° | 21.08 | 42.02 | -406.91 | 13.77 | 0.73 |
| φ5 = 0° | 2.39 | -3.83 | -47.23 | 148.78 | 51.64 | |
| 3 | φ3 = —90° | -22.63 | 42.21 | -408.22 | 14.20 | 0.58 |
| φ5 = 90° | 3.15 | -14.59 | -60.37 | 155.04 | 51.96 | |
| 4 | φ3 = 0° | -22.84 | 43.02 | -416.88 | 14.39 | 0.77 |
| φ5 = —90° | -2.18 | 3.00 | -170.39 | 112.58 | 50.51 | |
| 5 | φ3 = 0° | 22.06 | 42.73 | -406.00 | 13.67 | 0.70 |
| φ5 = 0° | 2.28 | -7.38 | 2.52 | 101.64 | 47.46 | |
| 6 | φ3 = 0° | -22.65 | 43.18 | -405.62 | 14.24 | 0.63 |
| φ5 = 90° | 2.98 | 1.83 | -153.83 | 117.94 | 46.60 | |
| 7 | φ3 = 90° | 21.03 | 41.05 | -406.34 | 13.58 | 0.71 |
| φ5 = 0° | 1.94 | -4.11 | -57.71 | 130.76 | 52.62 | |
| 8 | φ3 = 90° | -22.79 | 42.68 | -413.80 | 14.04 | 0.71 |
| φ5 = —90° | 1.06 | -6.76 | 48.09 | 129.60 | 55.34 | |
| 9 | φ3 = 90° | -22.05 | 42.62 | -409.69 | 13.63 | 0.55 |
| φ5 = 90° | 2.57 | -5.47 | -148.67 | 115.31 | 51.36 |
Figure 11.
Outer element average stress equivalent distribution
Figure 12.
Outer element average stress equivalent distribution
Figure 13.
Outer element total deformation distribution
Figure 14.
Outer element total deformation distribution
Figure 15.
Initial model (left) compared with the model after parametric optimization (right) in the same scale
Table 9.
FEM model parameters final values (input parameters: P1-P5 and Material model, output parameters: maximum stresses and masses of the parts)
| P1 [mm] | 12.8 |
| P2 [mm] | 15.5 |
| P3 [mm] | 26.5 |
| P4 [mm] | 49.3 |
| P5 [mm] | 40 |
| Material model | NanoCarbon (PA 12 + CF) |
| Max stress in inner part [MPa] | 12.9 |
| Max stress in outer part [MPa] | 25.6 |
| Inner part mass [kg] | 0.61 |
| Outer part mass [kg] | 0.48 |
Figure 16.
Final bearing model
Table 10.
Parameters of finite element models for validation of the design
| Element | No. of elements | No. of nodes |
|---|---|---|
| Inner part | 658,387 | 1,018,928 |
| Outer part | 211,159 | 360,405 |
Figure 17.
Outer element average stress equivalent distribution after parametric optimiation
Figure 18.
Outer element average stress equivalent distribution after parametric optimiation
Figure 19.
Outer element total deformation distribution after parametric optimiation
Figure 20.
Outer element total deformation distribution after parametric optimiation
Table 11.
FEM analysis summary after final design modifications
| Element | Outer | Inner |
| Max. stress for sliding element [MPa] | 6.24 | 12.49 |
| Max. stress for main element [MPa] | 20.59 | 28.50 |
| Max. displacement [mm] | 0.38 | 0.41 |
| Max. cylindrical displacement [mm] | 0.10 | 0.08 |
| Max. back surface displacement [mm] | 0.12 | – |
| Min. safety factor | 4.37 | 2.18 |
| Part with the lowest safety factor | Sliding | Sliding |