The Free-Leg Hexapod (Free-Hex) machine tool is an advancement from the conventional Stewart platform, which has the fixed base platform removed to enable the limbs to be attached to a wider range of surfaces (e.g. non-flat and curved). However, in some scenarios (e.g. in-situ repair of industrial installations), the limbs of the Free-Hex need to be attached to the surfaces with unequal stiffness, which brings the challenge of predicting the dynamics of the system for conducting machining operations under dynamically stable conditions. In this paper, after introducing the attachment stiffness (i.e. feet attached to the environment with different materials) in the conventional dynamic model of the parallel manipulator, the dynamic behavior of the Free-Hex machine tools devoted to the insitu operation environments was studied. Then, the experimental validation was conducted to prove the dynamic model developed in this paper. It was found that the errors of the proposed model are under 6% (i.e. 5.1% at symmetrical limb configuration and 5.8% at the arbitrary configuration) when the limbs are attached to the surfaces with unequal stiffness. Further, by applying the validated model, the dynamic performance of the Free-Hex with a wider range of attachment stiffness was analyzed. Overall, it was found that the attachment stiffness has a remarkable influence on the natural frequencies of the machine tool (e.g. the frequency of mode 4 at the symmetrical configuration is increased by 36.8% when the attachment stiffness of one limb changes from 0 to 1e+12 N/m). Thus, the work discussed in this paper can be utilized to avoid the dynamically unstable configurations of parallel kinematic machine tools (e.g. Free-Hex) when mounting on the surface with unequal stiffness in the in-situ operation environments.

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Parallel manipulators are increasingly utilized in extensive industrial applications due to their high accuracy, compact structure, and significant stiffness characteristics. However, most of the time, massive actuators are involved in constructing and controlling a parallel manipulator, which burdens the structure design and controller development. In this paper, a novel underactuated positioning system been built by different sets of linear motion units (defined as the positioning lines) is proposed, enabling to actuate the multiple degree-of-freedom manipulators with one motor. To achieve this, a smart shape memory alloy (SMA) clutch is presented to obtain the positioning function of each positioning line. Further, to get the decoupled motion regulation of the positioning lines, a new thermal kinematic model of the SMA clutch, which considers the heat dissipation influence on the metal components, was built and validated by the physical prototypes. The experimental results show that the constitutive model of the SMA clutch developed in this paper can be validated within the error of 5.3%. It can also be found that the heat dissipation of the metal component has a significant influence on the model accuracy of the SMA clutch (i.e., 2.6% of the model accuracy). The experiments on the underactuated positioning system produce the following results: the single positioning line can achieve high positioning (i.e., average error: 1.01%) and tracking (i.e., average error $\leq$ 1 mm) abilities; the underactuated positioning system can perform decoupled motions in the three positioning lines with high accuracy (i.e., ±2 mm within the stroke of 180 mm).

The original version of this chapter was revised. Mingfeng Wang was inadvertently not included as a coauthor. This has been corrected.