# Computational Methods for Deformable 1D Objects in Virtual Product Realization

Sammanfattning: In industry today, virtual design tools are used in the realization of a new product. As changes in the design and planning concepts are extremely costly in the later verification and production phases, much can be gained if a product design can be optimized and verified with respect to the assembly process with simulation tools as early as possible. A topic of special interest is the virtual preparation of deformable 1D objects such as electrical cables and wiring harnesses, hoses, pipes and tubes. They are geometrically characterized as one-dimensional in the sense that one dimension is significantly larger than the other two and can deform when subject to external forces and moments. These types of flexible components are usually located where there is restricted design space and are often associated with quality problems and late on-line adjustments due to geometrical interference. Hence, there is a strong motivation to further strengthen the virtual product realization process in this area. This thesis will present three computational methods for geometrical design and verification of deformable 1D objects. The main scientific challenge is to deal with the complexity of coupling a simulation model with iterative algorithms for optimization, path planning and variation simulation in an efficient way. The methods rely on a simulation model based on Cosserat rod theory that enables efficient and accurate computations of large spatial deformations of flexible 1D objects. The first method solves the problem of routing a deformable 1D object with respect to geometrical design constraints. The method is segregated in a deterministic grid search step and a simulation-based local optimization step. The second method solves the assembly verification problem for a deformable 1D object with a given design. If the verification is true, the method produces a smooth manipulation of a set of grip points that installs the object in the target configuration. The third and final method is in fact a methodology for performing analysis and visualization of geometrical variation in a deformable 1D object. Here, the main innovation is the construction of a discrete envelope for given tolerances based on convex hull computations and silhouette generation. Together, the three methods form a powerful tool set for geometrical design and verification. Quality problems and geometrical interference in the assembled product can now to a larger extent be addressed in the concept phase, thus saving significant development time and reducing the number of iterations between the design phase and the planning and verification phases. The methods are implemented as an integral part in the commercial software IPS Cable Simulation as of version 3.1 (2016).

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