Type synthesis and static balancing of a class of deployable mechanisms
Abstract
This thesis addresses the type synthesis and static balancing of a class of deployable
mechanisms, which can be applied in applications in many areas including aerospace and
daily life.
Novel construction methods are proposed to obtain the deployable mechanisms. First,
the type synthesis of the foldable 8-revolute joint (R) linkages with multiple modes is
presented. Two types of linkages are constructed by connecting planar 4R linkages and
spherical 4R linkages. The obtained linkages can be folded into two layers or four layers,
and have multiple motion modes. A spatial triad is also adopted to build single-loop
linkages, then the single-loop linkages are connected using spherical (S) joints or RRR
chains to obtain deployable polyhedral mechanisms (DPMs). The DPMs have only 1-
degree-of-freedom (DOF) when deployed, and several mechanisms with 8R linkages and
10R linkages have multiple motion modes and can switch modes through transition
positions. In addition, when connecting single-loop linkages using half the number of the
RRR chains, the prism mechanisms obtain an additional 1-DOF rotation mode.
Furthermore, the DPMs are developed into statically balanced mechanisms. The
geometric static balancing approaches for the planar 4R parallelogram linkages, planar
manipulators, spherical manipulators and spatial manipulators are developed so that the
mechanisms can counter gravity while maintaining the positions of the mechanisms. Only
springs are used to design the statically balanced system readily, with almost no
calculation. A novel numerical optimization approach is also introduced which adopts the
sum of squared differences of the potential energies as the objective function. Using the
proposed static balancing approaches, the 8R linkages and the DPMs presented in this
thesis can be statically balanced.