# An Extended Functional Design Approach Based on Working Principle and Property and Its Application
## 3 Working Principle and Property
### Property Relationship  
The reason why a cutting tool used in machining can be employed to remove material from the machined object is that there is an obvious difference in hardness between the cutting edge of the cutting tool and the machined object. In this case, the realization of function (remove + material) is mainly related to the different values of a common property (hardness). The property and the property relationship are vital to realizing a function. The property relationship describes how two design objects interact with each other. For property \(i\) of object A and property \(j\) of object B, the relationship between property \(i\) and property \(j\) can help to realize the goal function. For example, the external thread of the screw and the internal thread of the screw hole can only screw together to realize their connection function when the characteristic parameters of the external thread and the internal thread are the same. In the following section, this paper will discuss the property relationship between inherent properties and designed properties. Figure 4: Several mapping examples between the working principle and the property. Figure 3: The mapping model between the working principle and property. The property relationship of an inherent property includes the comparison relation (\(CR\)) and existence relation (\(ER\)). The former indicates that the value of the same inherent property of two design objects can be compared numerically; the latter indicates whether two design objects have a certain common property. \(CR\) can be described as a triple: \(CR=\langle attr_{i}^{A},\ operator, attr_{i}^{B}\rangle\). It includes the inherent property \(i\) of design object A (\(attr_{i}^{A}\)), the same inherent property \(i\) of design object B (\(attr_{i}^{B}\)), and a comparison operator. The comparison operator has three forms (\(>\), \(<\), and \(=\)). \(ER\) is a binary group and can be described as: \(ER=\langle\left(attr_{i}^{A},1/0\right),\left(attr_{i}^{B},1/0\right)\rangle\). The existence of \(attr_{i}^{A}\) is described by \(\left(attr_{i}^{A},1/0\right)\), where 1 represents the fact that design object A has property \(i\), while 0 indicates that design object A does not have property \(i\). The property relationship of designed properties includes the geometric dimension constraint relationship (\(GDCR\)) and the spatial position constraint relationship (\(SPCR\)). \(GDCR\) indicates that there should be an appropriate geometric dimension relationship between directly related designed properties, such as the dimensional constraint relationship between the key and keyhole. \(GDCR\) aims to ensure the assembly rationality between design objects. \(SPCR\) refers to the appropriate relative spatial position relationship between two directly related designed properties, such as the coaxial constraint relationship between the hole and the axis. \(SPCR\) aims to limit the spatial degree of freedom of the design object, to ensure that the object has definite action opportunities. Once the relative spatial position relationship between two directly related design objects is effectively limited (i.e., the spatial degree of freedom of the design object is limited), the action object will naturally produce the expected execution action, given the input variable. \(GDCR\) can be described as a triple: \(GDCR=\langle\langle attr_{j}^{A},AP^{Aj}\rangle,\ operator,\langle attr_{k}^{B},AP^{Bk}\rangle\rangle\). It includes the associated parameter \(AP^{Aj}\) of the designed property \(attr_{i}^{A}\), a comparison operator, and the associated parameter \(AP^{Bk}\) of the designed property \(attr_{k}^{B}\). The comparison operator has three forms (\(>\), \(<\), and \(=\)). \(SPCR\) can also be described as a triple: \(SPCR=\langle\langle attr_{j}^{A},AF^{Aj}\rangle,\ \langle attr_{k}^{B},AF^{Bk}\rangle, PRE_{l}\rangle\).