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This lecture covers the principles of flexible guidances in mechanisms, focusing on rectilinear movements and suppression of internal degrees-of-freedom. Topics include compound parallel spring stages, corner cube mechanisms, rectilinear mechanisms based on membranes, corner-blades, and circular mechanisms. The instructor discusses various mechanisms such as Sarrus mechanism, flexure-based mechanisms, and butterfly pivot, emphasizing factors like stroke, lateral error, and radial stiffness. The lecture also delves into the design considerations for rectilinear motorized axes, highlighting the optimization of pivots for ultra-high precision. Additionally, it explores the application of these mechanisms in space exploration instruments, specifically in the context of the European Mars Mission EXOMARS and the CLUPI instrument. The presentation concludes with insights on torsion bars and their torsion stiffness.