# A New Concept Compliant Platform with Spatial Mobility and Remote Actuation
## 1 Introduction  
A parallel architecture offers several advantages to the designers of spatial platform mechanisms. In fact, they rely on a multi-loop topology that is certainly convenient for the stage stiffness and accuracy, whereas their forward kinematic analysis becomes more complex. The Stewart-Gough platform, a mechanism that can be considered to be a milestone of parallel manipulators, was presented in 1965 [1]. This six-DoF (degree of freedom) system can be controlled in any combination by six motors and has the advantage of no fixed axis relative to the ground. Classical issues for parallel manipulators have been extensively studied in the literature, such as structural kinematics [2], workspace [3], singularity [4], optimal design [5], structure synthesis [6], manipulability [7], control of redundantly-actuated [8], and remotely cable-driven parallel manipulators [9]. On the other hand, more recent subjects have still not been well investigated for parallel platforms, such as connectivity and redundancy [10], topology [11], and planarity [12]. Classical parallel platforms are composed of rigid links and ordinary kinematic pairs with a geometric closure configuration. However, they could be built as compliant mechanisms [13; 14; 15], which present a series of advantageous characteristics: they are not subject to backlash and do not need lubrication; they can be also built from a unique block of material; and finally, they have generally a neutral or balance configuration from which the deformed poses can be achieved. In fact, they can reach a given configuration thanks to external forces that can be applied with a high precision to deform the elastic structure, using also a redundant driving strategy. More recently, active compliance [16; 17] has been added as a further possibility in design, acting both as a series or in a parallel configuration with passive compliance. These features make compliant mechanisms very interesting for applications where lubrication is impossible or where extreme accuracy is needed. For these reasons, a group multi-DoF compliant stages has also been developed in literature [18]. Since 1990, stiffness and conditioning maps of the workspace of parallel manipulators have been established [19], in order to prevent special types of singularities, which result in a loss ofcontrollability. A six-DoF force sensor was designed in 1991 [20] on the base of the Stewart-Gough platform. In this layout, the fixed and mobile platforms are coupled by six spring-loaded pistons, whereas the length variations are measured by means of six linear voltage differential transformers mounted along the pistons. The Stewart-Gough inverse and forward kinematic transformations are used to calculate the forces and torques that are applied to the mobile platform. A three DoF translational compliant parallel platform was presented in 2005 [21] for nanomanipulation. Workspace, dexterity, and isotropic configurations were studied by using the pseudo rigid-body model (PRBM). A six-PSS (prismatic-spherical-spherical) nanopositioner compliant mechanism was designed [22] to be actuated by means of six multilayered piezoelectric actuators. The system is composed of one fixed plate, three two-PSS compliant mechanisms, and one end effector. The PRBM is also used in this investigation to study its kinematic analysis. A three DoF spatial translational accurate positioning compliant platform with flexible hinges and with piezoelectric actuators has been designed [23] to achieve high stiffness, a high speed of dynamic response, high kinematic accuracy, and high resolution. A six-DoF compliant parallel micro-scale manipulator with piezo-driven actuators and integrated force sensor has been designed [24] to provide real-time force information for feedback control. Kinematic and static analysis were investigated to achieve high positioning accuracy, compactness, and smooth and continuous displacements.