Theoretical dry test
3.2 Pixel checker tool
The checking tool checks the object in two steps. The tool first uses the forward kinematic model to exclude any pixels that are placed deep within the reach. Then the inverse kinematic model will check the critical pixels to insure reachability. This tool is created in Matlab, and will be converted to a Visual Basic solution in chapter4. Validation of the tool is done by executing different types of tests by the robot and tool. The tool requires the following parameters to determine the exact location of the model relative to the robot:
Tool length and offset;
Workobject position and orientation1;
Robot type, link lengths and axes limitations.
3.2.1 Forward kinematic model
The forward kinematic model is used to create the section of the reach dome similar to figure 3.3. It is able to offset a certain length as stated in subsection 3.1.1. The type of robot will determine the link lengths and the axes limitations that will create the shape of the section. The tool parameters will shift the dome into the correct position relative to the robot base. The workobject will determine the position and orientation of the loaded model relative to the robot and the section.
1Origin position and orientation
The offsetted section will be used to evaluate the pixels if they are located outside this dome.
This is done by calculating the vector length and angle towards the XY -plane2 of each pixel relative to the robot base. In a similar way as stated in subsection3.1.1the pixels are evaluated to check which pixel is inside the offsetted reach. The pixels which are located inside the reach are discarded. The set that is in the ”danger” zone will be evaluated by the inverse kinematic model. If the size of the rejected set is equal to 0, then every pixel fits within the safety zone so, the model is printable and does not need further inspection by the inverse kinematic model.
3.2.2 Inverse kinematic model
The set of pixels that is rejected by the forward kinematic model needs a second inspection by the inverse kinematic model because the check with the forward kinematic model is not exact. For this inspection, the equations2.13to2.19from subsection2.4.1are used. The input of the equations are the orientation and position of the pixels, relative to the base of the robot. If the equations can be solved and the result of the equation fits within the boundaries of the axes limitations, then the pixel is reachable from the current position. The whole set is evaluated by the inverse kinematic model, unless the model finds a pixel that is not reachable. Then the calculation is aborted and it is not possible to print this model without changing the current parameters. If the whole set is evaluated and no pixel is found outside the boundaries, then the model is printable with the current parameters.
3.2.3 Validation of the tool
The validation of the tool is done by checking 5 objects that are made to test the edge of the reach dome. Three tests to validate the first step - the forward model - and two tests to validate the second step - the inverse model.
The forward model will be tested by taking a part of the dome reach and offsetting this 15 mm inwards and outwards. The inner part needs to be within the range and the outside part cannot be reached. This is visualized in Matlab. The offset3 of the dome will be 0 to check if the inner part is within the reach as visualized in figure3.7and the outer part is out of reach as visualized in figure 3.5. The black line in figures3.5, 3.6and 3.7 represents the cross section of the reach from figure3.3. A third check is done to validate the offset by setting the margin to 50 mm and rechecking the inner part. This test is visualized in figure3.6, the inner part that was previously in the safe zone is the danger zone. The blue parts in figure3.5and3.6are pixels that are located deeper inside the range, those pixels are reachable. These pixels are the seam where the printer jumps from layer to layer.
2Leveled floor.
3Margin.
Figure 3.5: Outer object with margin set to 0.
Figure 3.6: Inner object with margin set to 50 millimeter.
Figure 3.7: Inner object with margin set to 0.
The pixels that are located in the ”danger” zone will be checked by the inverse kinematic model. It is not possible to generate a visualisation of these models. As expected the outer shell is not reachable. The inner shell that was only in the ”danger” zone and not out of bounds, is completely reachable. This shows that the kinematic models are applied correctly and the previous tests validate the tool.
3.3 Conclusion
The tool created in section 3.2 uses a forward kinematic model to determine which pixels are located ”deep” inside the range. The pixels that are not within this area will be passed on for further inspection by the inverse kinematic model that is able to check exact if a pixel is in range or not. If a single pixel is found to be out of range then it is not possible to print that object.
The pixel checking tool is validated in section 2.5 and is found to be working correctly. The software that is developed in chapter4 will be based on the pixel checker tool from section3.2.