Layouts of spatial motion structures 151
7.5 Conclusion and discussion
A tessellation method to build motion structures using repeated building
blocks and tiling technique is presented in this chapter. It involves three
steps: selection of suitable tilings, construction of building blocks using
common or overconstrained mechanisms and validation of geometrical
compatibility. The first two steps have to be taken jointly and it may possibly involve many design iterations.
This method has been applied to the assemblies consisting of Bennett
linkages, Myard linkages and threefold- symmetric Bricard linkages, respectively. All three regular tilings (3
6
), (4
4
) and (6
3
), have been adopted and a
number of building blocks of different types have been discussed. Some of
the motion structures that have been described in previous chapters have
been reconstructed by this tessellation method.
It should be pointed out that there are many ways of constructing building blocks, including those made from a combination of more than one
type of three dimensional overconstrained linkages. Great care has to be
taken in design of a building block as its motion could have profound
influence on the overall performance of the assembly. For instance, if
compact folding is the objective, the building blocks themselves have to
exhibit this property. Furthermore, once a design is obtained attention has
to be paid to the size and shape of the links and details of the joints for a
desirable folding configuration may not be realised due to intersection of
links.
Only regular and uniform tilings and edge- to-edge tilings are utilised
here. Nevertheless this approach seems to yield useful results judging by
the successful examples illustrated here. Readers are encouraged to explore
other tilings and patterns that can be found from references such as Grünbaum and Shephard (1986).
Figure 7.14 A building block based on the threefold-symmetric Bricard linkage
with twists of π /3 or 2π /3.
7.5 Conclusion and discussion
A tessellation method to build motion structures using repeated building
blocks and tiling technique is presented in this chapter. It involves three
steps: selection of suitable tilings, construction of building blocks using
common or overconstrained mechanisms and validation of geometrical
compatibility. The first two steps have to be taken jointly and it may possibly involve many design iterations.
This method has been applied to the assemblies consisting of Bennett
linkages, Myard linkages and threefold- symmetric Bricard linkages, respectively. All three regular tilings (3
6
), (4
4
) and (6
3
), have been adopted and a
number of building blocks of different types have been discussed. Some of
the motion structures that have been described in previous chapters have
been reconstructed by this tessellation method.
It should be pointed out that there are many ways of constructing building blocks, including those made from a combination of more than one
type of three dimensional overconstrained linkages. Great care has to be
taken in design of a building block as its motion could have profound
influence on the overall performance of the assembly. For instance, if
compact folding is the objective, the building blocks themselves have to
exhibit this property. Furthermore, once a design is obtained attention has
to be paid to the size and shape of the links and details of the joints for a
desirable folding configuration may not be realised due to intersection of
links.
Only regular and uniform tilings and edge- to-edge tilings are utilised
here. Nevertheless this approach seems to yield useful results judging by
the successful examples illustrated here. Readers are encouraged to explore
other tilings and patterns that can be found from references such as Grünbaum and Shephard (1986).
Figure 7.14 A building block based on the threefold-symmetric Bricard linkage
with twists of π /3 or 2π /3.