Over the last two decades, reconfigurable mechanisms have become one of the most important research topics in robotics due to their multiple functionalities on a sole machine that can fulfil a variety of tasks. They are more effective in many aspects than traditional sole-function mechanisms. There are different types of reconfigurable mechanisms such as kinematotropic mechanisms, metamorphic mechanisms, discontinuously moveable mechanisms, mechanisms with multi-furcation, and multi-mode reconfigurable mechanisms (MMRMs).

This dissertation focuses on MMRMs that include single-loop multi-mode reconfigurable mechanisms (SLMMRMs) and multi-loop multi-mode reconfigurable mechanisms (MLMMRMs), and mainly deals with the design and kinematic analysis of new SLMMRMs. Fruitful results have been achieved on SLMMRMs that have single DOF (degree of freedom) or variable DOFs with two operation modes in the literature. However, it is still an open issue to design new type of SLMMRMs with more operation modes and to conduct effective kinematic analysis of these mechanisms.

Apart from investigations of various reconfigurable mechanisms, the kinematic analysis methods for serial and parallel mechanisms are also revisited. The multidimensional geometry in conjunction with advanced algebra is found to be very effective in dealing with the kinematic analysis of MMRMs. The synthesis of constraint equations of typical serial kinematic chains, as compositional units of closed-loop/parallel mechanisms, is undertaken using both explicitation and implicitization approaches based on the kinematic mapping method. A linear algebraic method is applied to select the proper number of constraint equations for a serial kinematic chain, which is an important step in the kinematic analysis of a mechanism using the implicitization approach. Moreover, the transformations in the base and moving platform of a parallel mechanism are defined and unified into serial kinematic chains (legs) to generate the parallel mechanism’s constraint equations.

Based on the investigation of single-loop overconstrained mechanisms (SLOMs) and the research on existing type synthesis methods, this dissertation presents three methods for constructing 7J (J:​ joint) SLMMRMs that have three or more operation modes. Nineteen classes including three new classes of 7J SLMMRMs are presented using the first method. 7J SLMMRMs can be classified according to their numbers of active joints in different operation modes:​ 7J SLMMRMs with two types of operation modes and 7J SLMMRMs with three types of operation modes. The procedures of the second method to produce a 7J SLMMRM that has three operation modes but two kinds of operation modes are illustrated. Two 7R SLMMRMs are generated by combining two same Bennett linkages in different R-joint orders to form 6R (R:​ revolute) SLMMRMs followed by inserting one new R joint. They are verified by CAD modes that they have two Bennett linkage modes and one 7R mode.

Two novel 7R SLMMRMs are also designed according to the third method where each configuration is obtained by inserting an R joint into a 6R SLOM with one or two operation modes. The first 7R SLMMRM produced by inserting an R joint to the well-known Sarrus linkage has three operation modes but two types:​ one 6R mode and two 7R modes. The second 7R SLMMRM constructed by inserting a new R joint to a line and plane symmetrical Bricard linkage with two operation modes has four operation modes but three types:​ one 4R mode, two 6R modes and one 7R mode. The kinematic analysis of the two 7R SLMMRMs have been completed using both the explicitation approach and algebraic method, which produces the plotting of their operation mode curves. The transition configurations are also identified. These results are further verified by CAD models and 3D printed prototypes.

Many configurations of 7J SLMMRMs that have three or more operation modes satisfying multiple target requirements can be generated and analyzed according to the theoretical foundation in this dissertation.