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The dynamic design for space over three-dimension is a tough problem in mechanical design, because there are no proper cognition and analysis methods for multi-dimensional space. So, more abstract and comprehensive methods are in need. Normed function space theory is a fully-fledged mathematics theory for multi-dimensional space, which is a powerful aid in analysis and representation. By using arbitrary function, dynamic design problem can be solved, such as the description of multi-variable system, relation modeling and optimization. Variable systems with totally different physical meanings may have an identical norm function structure, which makes the abstraction and analysis of complex problem easier. The design is the modeling based on physical essence and the analysis and calculation of model, instead of traditional geometry analysis. The method is not analogy but precise calculation, which can produce an optimum solution in norm function. Centrifugal governing system is a typical mechanical power system. According to dynamic requirement, the energy arbitrary function is set up and solved. That completes the mechanical structure design. The example shows, the arbitrary function design is workable and digitized.