Spatial motion structures based on the Bennett linkage
Designing a large motion structure has different priorities from designing a machine. There are two keys to a successful concept. First, to identify one of a small number of robust and scalable building blocks made of known mechanisms, and, second, to develop a way by which the building blocks can be connected to form a large assembly while retaining the mobility of each mechanism. Motion structures developed over the past three decades are based mostly on planar mechanisms, such as those introduced in Chapters 3 and 4. It is rare to use truly three dimensional mechanisms. The reason is primarily because the majority of structural engineers are less familiar with the three dimensional mechanisms. In this chapter, we shall introduce types of motion structures that are constructed by tessellation of the Bennett linkage. The kinematics of Bennett linkage has been summarised in Chapter 2, including its geometrical features and closure equations. As a spatial fourbar linkage, a typical Bennett linkage, Figure 5.1(a), consists of a closed chain of four bars which span the shortest distance between two axes of adjacent revolute joints. Each of the bars has lengths and twists identical to those of the bar which is not directly connected to it. It therefore can be represented schematically by a rectangle shown in Figure 5.1(b). Each side of the rectangle corresponds to a link; at every corner where two links meet is a revolute joint represented by a black dot. Twists of each link are given alongside the respective bars. This simplified diagram will be used throughout this chapter to avoid confusion in drawing real three dimensional assemblies. In the next section we shall use the Bennett linkage as the building block to construct large motion structures.