# Upper Limb Orthoses: Integrating Topology Optimization and 3D Printing for Custom Fit and Function
## 4 Design Process for Custom Limb Orthoses
### Manufacturing Constraints
#### 4.3.2 Minimum Member Size Control--MINDIM  
The parameter MINDIM is used to ensure that designs are both discrete and manufacturable, by defining the minimal acceptable dimensions for structural elements [12; 15; 16]. As illustrated in Figure 8, the MINDIM values chosen for each analysis vary. In the case of coarse meshes, the MINDIM values span from 2.5 to 10.1. For fine meshes, they fall within the range of 1.7 to 6.9 [27]. Figures 12-14 compare the results of non-use, and the implementation of Checkerboard control (CHECKER) and Minimum Member Size Control (MINDIM) for splint models with coarse and fine FE mesh. It is important to mention that applying the MINDIM constraint automatically activates the CHECKER parameter, while additionally increasing the value of the \(DISCRETE\) parameter from 1 to 2. The \(DISCRETE\) parameter essentially represents the penalty factor \(p\), mentioned in Section 2, used to penalize the intermediate density elements in each design, in order to produce more distinct solutions, which are easy to manufacture. The DISCRETE parameter in Optistruct is related to the penalty factor, \(p\), as follows: \(DISCRETE=p-1\). Therefore, in the case where the DISCRETE parameter takes the value 2, when the MINDIM constraint is applied, this means that \(p=3\), which is a typical value of the penalty factor for solids. Also, applying the MINDIM constraint automatically increases the number of maximum iterations that can be performed until convergence is achieved in the solution of the TO problem. The default value is 30, and the maximum number of iterations is automatically increased to 80 when the MINDIM parameter is used. From the results of the optimal designs presented in Figures 12-14, it is observed that the application of the additional CHECKER parameter as well as the MINDIM constraint gradually leads to more distinct solutions. These solutions, especially in the case of a combined application of the two aforementioned parameters, simultaneously setting a higher value (equal to 5.0) to the MINDIM parameter, are structurally easier to implement through 3D printing technology. For the first two load cases studied (radial deviation and wrist flexion), it is observed that the use of the denser FE mesh plays an important role in achieving wrist splint designs, which are characterized by more discrete structural members, and in particular when the denser grid is combined with the application of constraints to control the checkerboard distribution and to reduce elements with intermediate density. Another observation based on these results is that the application of the aforementioned constraints results in an increase in the number of iterations until convergence is achieved in the solution for each TO problem; nevertheless, the final optimal designs of the wrist braces are design-wise and manufacturability-wise much better compared to those in which the above restrictions were not applied. Figure 12: Load Case 1. Volfrac 25%. Comparison of results of not using as well as applying the CHECKER and MINDIM parameters to the splint models with (**a**–**h**) the coarse and (**i**–**p**) the fine FE mesh. Figure 13: Load Case 2. Volfrac 25%. Comparison of results of not using as well as applying the CHECKER and MINDIM parameters to the splint models with (**a**–**h**) the coarse and (**i**–**p**) the fine FE mesh. The topologically optimized wrist splints illustrated in Figures 12l,p, 13l,p, and 14d,h exhibit several advantages over classically constructed splints that are widely used for the treatment of metacarpal fractures. The material removed from the original models, which, based on the results of this work, is observed to reach 25% of the original volume, leads to final designs of wrist splints that are considerably lighter, while at the same time exhibiting high strength. The creation of the holes in specific patterns that follow the paths of the loads for each case being studied increases the levels of aesthetics, while also enabling sufficient ventilation and cleaning of the hand.