**4.1 Analysis of robot for laparoscopic surgery**

A surgical robot needs very well-prepared documentation that includes many chapters about:


## *4.1.1 Workspace*

The workspace is the entire space around the "home" position where the robot can move. This is the robot workspace. The evaluation of the workspace is done by knowing the direct kinematics equations for a robot with configuration based on parallel structures (see **Figure 6**). Such workspace is presented in gray color in **Figure 6**-b with a section in red color. But near this workspace should be added the

#### **Figure 7.** *Robot workspace evaluated with Solidworks API.*

required space on design. This space is presented in green color, which is a special workspace in the sense that its definition is made in cylindrical coordinates. This type of workspace has a number of advantages in terms of solution symmetry and the disadvantage that the implementation of its equations is complex.

The workspaces above were evaluated using the MATLAB program based on a parametrization in the position of the platform using only generalized displacement at its center. These mathematical equations can also be implemented in a CAD program in order to benefit from all its graphical performance. A such example is in **Figure 7**, which shows the workspace of a hexapod robot evaluated using procedures developed with the Solidworks API. The working method uses the procedures presented in [17] to find the boundary of the workspace at the operating limit of the actuators.

API (Application Programming Interface) is a background support program from Solidworks CAD that allows programming commands to be written in a specific language to automate model execution based on procedures implemented internally in software.

The methods presented for a robot's workspace do not take into account the possible collision between the elements of the system when positioning in workspace. Because the actual geometry of the components can vary greatly from the idealized shape, then it is necessary to implement collision detection procedures.

#### *4.1.2 Collision detection*

A robot is generally a machine designed to perform tasks automatically, with speed and accuracy. Even when a robot is operating properly, it may collide with people or objects that enter its workspace and may even cause personal injury or damage to those objects. A particular case is the self-collision when the robot strikes its own components from which it is built [18, 19].

Injuries or damage to others (humans or mechanical components) due to the robot's activities are classified as contact damage. The main aspect of the impact between two or more components is collision detection. How collision assessment depends mainly on the geometry of the parts, the more complicated are the components, then more

#### **Figure 8.**

*A short presentation of decomposition techniques used in collision detection [20].*

#### **Figure 9.**

*Collision detection strategy at forbiden zones. (a) virtual reprezentation of liver (b) veno-arterial tree in tubes geometric primitives.*

time it takes to assess possible collisions. That's why it's a good idea to start with a simplified geometry. **Figure 8** summarizes the geometry decomposition techniques used in collision detection. In paper [20], the authors presented some innovative techniques for the detection of collisions between components with complex geometry.

If the assessment of the collision is done with a veno-arterial network then the detection becomes even more complicated. For the speed of the calculations, it is recommended to simplify an artery tree until to the level of geometric primitives (**Figure 9**).

The Solidworks software is useful in collision detection with its methods to evaluate the distance between components.

#### *4.1.3 Kinematic performances*

Evaluating the configuration of a robot involves a study of choosing the best features (dimensions, types of links, type of drives, etc.) according to different criteria, such as:


The optimization of the different quality parameters of the robot must be done according to several kinematic performance criteria (see **Table 1**): singularities, determinants of the inverse of the Jacobian matrix, dexterity, global conditioning index, local conditioning index, manipulability, etc. [21, 22].

Optimization of configuration (see **Figure 10**) involves the knowledge and use of advanced methods of mathematical calculation: multi-criteria methods, genetic algorithms (GA), and matrix processing. **Figure 10**-b shows the dispersion of intermediate results when using a GA to optimize the configuration of a hexapod robot until the optimal position is found.

The kinematic evaluation of the mechanisms can also be done using a professional CAD program. Solidworks provides tools for such assessments. **Figure 11** shows the final results of the positions of a surgical robot using the Solidworks software for both the forward and inverse kinematics. **Figure 11**-a shows the results of forwarding kinematics procedures by increasing the length only at one actuator, and **Figure 11**-b shows the results of inverse kinematics procedures to put the tools at a specific


#### **Table 1.**

*Criteria for kinematic performances.*

**Figure 10.**

*Assessment and optimization of kinematics. (a) assessment of configuration in real time (b) optimization using GA.*

**Figure 11.** *Assessment of kinematics using Solidworks. (a) forward kinematics (b) inverse kinematics.*

location in a specific direction. However, the methodology requires knowledge of the Solidworks API script.

## *4.1.4 Durability assessment*

Effective service life is determined by several factors, including:


Research results on evaluation of the effect certain expected loads on the service life of a product do have. A load cycle was considered. The stress level is VonMises stress extracted from 100 load cases at the same probe when the loads vary in different directions and amplitude. An example of VonMises stress level at probe for load case (no. 55) with 1000 N at tool is presented in **Figure 12**. The probe is located at platform because this part is the main for structural design optimization.

Material for platform is considered in this phase the polycarbonate plastic material. This material could be changed during further optimization steps.

The assessment of the endurance by effect of the stress state on the material took into account the Wohler curve of the polycarbonate plastic by applying the rainflow method. The results are shown in **Figures 13** and **14**. For the above load cycle the damage is 1.0434e-6 for a single stress sequence. This means that the life of the verified component is 958,405 cycles.

Rainflow algorithm is the most popular counting method used in fatigue and failure analysis for lifetime estimation of mechanical parts. The rainflow counting technique was introduced by Matsuishi and Endo in 1968 to extract closed loading

**Figure 12.**

*Von Mises stress level at probe for load case (no. 55).*

**Figure 13.** *Reference load cycle.*

reversals or cycles for a correct estimation of fatigue. The "rainflow" was named in comparison to the flow of rain falling on a pagoda roof [23, 24]. For the studied example, the detailed rainflow diagram is presented in **Figure 15**.

Endurance evaluation can be done also using Solidworks software, but not with such detailed diagrams for post-processing and reports but with something else which is also important – durability in 3D fields.

### *4.1.5 Thermo-mechanical evaluation*

Thermal flow can influence the performance of a robot. These aspects are even more important in the case of a surgical robot. The results of thermo-mechanical

*New Trends in Robots Engineering with Professional Software SolidWorks DOI: http://dx.doi.org/10.5772/intechopen.105979*

**Figure 14.** *Fatigue curve for plastic -polycarbonate.*

**Figure 15.** *Rainflow diagram.*

simulation for the surgical applications hexapod robot are further presented. Thermal load is considered overheating of an actuator from 18 to 30 degrees Celsius because of a failure at its motor. Because of to this thermal load, the total deviation at the end of the tool is 0.25 mm for presented model (see **Figure 16**).

In a surgical room, there could exist many thermal sources from the heating of electrical systems, heating flow, radiation, convection, advection, etc. An evaluation of thermal effects is mandatory for a surgical robot.

#### *4.1.6 Damage detection*

Structural Health Monitoring (SHM) is applied today to mechanical structures that require significant costs, for structures difficult to inspect or where human safety is a priority. The main task in this subject is damage detection. But damage detection involves today also methods to estimate damage location, damage size, or other additional information about the damaged area.

In this sub-chapter is presented an improved DLAC method for damage localization technique applied to a surgery robot structure. Basically, method use frequency

**Figure 16.** *Thermo-mechanical analysis. (a) thermal field (b) thermal deformation.*

shift for damage detection (Eq. (2)). The DLAC criterion was improved by transform equation into a probability index for a better assessment (Eq. (3)).

$$DLAC(i) = \frac{\left|\Delta \text{o}\_E^T \Delta \text{o}\_A(i)\right|^2}{\Delta \text{o}\_E^T \Delta \text{o}\_E \left(\Delta \text{o}\_A^T(i) \Delta \text{o}\_A(i)\right)}\tag{2}$$

where Δω<sup>X</sup> is the frequency shift for analytical or experimental (A, E) model.

$$\text{probability}(\text{DLAC}) = \text{RESCALE}(\text{DLAC}, \mathbf{0}, \mathbf{100}) \tag{3}$$

Successful damage localization technique depends on eigenmodes number. In **Figure 17** there are presented the set damages locations and final diagram for DLAC probability index.

The probability index of DLAC criterion shows the maximum value exactly where the damage was imposed in each model. This is possible when exist only one damaged area. In case of simultaneous existence of several damages, the DLAC method is no longer effective, being necessary to corroborate with other criteria for a correct evaluation.

**Figure 17.**

*Damage localization using 10 eigenmodes. (a) 8 damaged locations (b) DLAC probability index assessment.*

*New Trends in Robots Engineering with Professional Software SolidWorks DOI: http://dx.doi.org/10.5772/intechopen.105979*

Detailed examples for damage detection probability index can be found in [25]. The complete task of the simulations for surgical robot was developed based on MATLAB software [26], SOLIDWORKS Educational [27] and user defined programming routines, VB, API, etc., [28].

#### **4.2 Damage detection for robotic arm**

A similar damage localization technique was tested on the robotic arm of the visually impaired mechatronic system (see **Figure 2**. (a)). The simulation uses 8 eigenmodes and 6 damages.

One can conclude that simulation results prove the estimation for the damage location, as the higher probability of damages resulted for location no. 5 (see **Figure 18**).

### **4.3 Optimization of geometric configuration for a hand prosthesis finger**

The model of finger hand prosthesis has been built, as part of a research on biomechanical prosthesis (see **Figure 19**) and one important step prior to prototyping was that of optimization its geometry, specially its mechanical components (levers) dimensions.

*Damage localization using 8 eigenmodes. (a) serial robot - 6 damages (b) DLAC probability index.*

**Figure 19.** *Hand finger's motion. (a) finger model (b) real finger.*

**Figure 20.** *Hand finger components. (a) tip finger trajectory (b) finger prototype.*

Basic finger's motion is that of rotation of phalanges so that to grab an object. Based on the 3D model, the fingertip trajectory was simulated (so that to be on a circle arc) and thus the position of the pressure sensor was determined (see **Figure 20**) at a radius of 32 mm. In the 3D model, the sensor is positioned at 28 mm. So, adjustments of levers' lengths have to be done.
