<p>This thesis studies path generation for industrial robots of six degrees of freedom. A path is defined by connection of simple geometrical objects like arcs and straight lines. About each point at which the objects connect, a region, henceforth called a zone, is defined in which deviation from the defined path is permitted. The zone allows the robot to follow the path at a constant speed, but the acceleration needed may vary. </p><p>Some means of calculating the zone path as to make the acceleration continuous will be presented. In joint space the path is described by the use of cubic splines. The transformation of the Cartesian path to paths in joint space will be examined. Discontinuities in the second order derivatives will appear between the splines. </p><p>A few examples of different zone path calculations will be presented where the resulting spline functions are compared with respect to their first and second order derivatives. An investigation of the number of spline functions needed when, given an upper limit of deviation, the transformation back to Cartesian coordinates is made.</p>

This thesis studies path generation for industrial robots of six degrees of freedom. A path is defined by connection of simple geometrical objects like arcs and straight lines. About each point at which the objects connect, a region, henceforth called a zone, is defined in which deviation from the defined path is permitted. The zone allows the robot to follow the path at a constant speed, but the acceleration needed may vary. Some means of calculating the zone path as to make the acceleration continuous will be presented. In joint space the path is described by the use of cubic splines. The transformation of the Cartesian path to paths in joint space will be examined. Discontinuities in the second order derivatives will appear between the splines. A few examples of different zone path calculations will be presented where the resulting spline functions are compared with respect to their first and second order derivatives. An investigation of the number of spline functions needed when, given an upper limit of deviation, the transformation back to Cartesian coordinates is made.

Yes / In engineering design, there are many functional relationships which are difficult to express into a simple and exact mathematical formula. Instead they are documented within a form of line graphs (or plot charts or curve diagrams) in engineering handbooks or text books. Because the information in such a form cannot be used directly in the modern computer aided design (CAD) process, it is necessary to find a way to numerically represent the information. In this paper, a data processing system for numerical representation of line graphs in mechanical design is developed, which incorporates the process cycle from the initial data acquisition to the final output of required information. As well as containing the capability for curve fitting through Cubic spline and Neural network techniques, the system also adapts a novel methodology for use in this application: Grey Models. Grey theory have been used in various applications, normally involved with time-series data, and have the characteristic of being able to handle sparse data sets and data forecasting. Two case studies were then utilized to investigate the feasibility of Grey models for curve fitting. Furthermore, comparisons with the other two established techniques show that the accuracy was better than the Cubic spline function method, but slightly less accurate than the Neural network method. These results are highly encouraging and future work to fully investigate the capability of Grey theory, as well as exploiting its sparse data handling capabilities is recommended.

本研究可分為兩部份，第一部份以CBD為中心，向外擴展之地價空間結構變化情形之測試，主要是方法上的應用。運用較富彈性且能符合多核心都市測試需要之三次雲形函數來測試台北市之地價空間結構。研究發現都市發展方向會影響地價空間結構之變化，而傳統單核心模型之單一核心之假設及無考慮方向性，並不能充份描述現代大都市之真實空間結構。 　　第二部份則為了解各核心對地價影響情形，及在空間上互動關係進行多核心模型之測試。研究發現地價為都市空間中多核心互動的結果。而相同屬性、規模的核心間有排斥效果，不同屬性、規模的核心間則有吸引效果。藉由多核心之分散健全發展，與交通建設之密切配合，將可使都市之地價及都市空間結構更加健全發展。 / This research is divided to two parts. First part is to test the structural variance of the land price which extends by CBD. The method, the cubic spline function, is flexible and it can match the need of the polycentric city. From the test, we find the different directions which will affect the spatial structural variance of the land price. But the factor of the direction isn't included in the hypothesis of the traditional monocentric model, and it can't be described the true spatial structure of modern city sufficiently. 　　Another is the test that to understand the land price variance situation by the different centers and the interactions of them.By this test, it shows that land price is the result of the polycentric interactions of urban spatial structure. We also find there is a repelling effect between the same character and scale centers; vise versa.