The compliant version of the 3-RRR spherical parallel mechanism known as "Agile-Eye": Kinetostatic analysis and parasitic displacement evaluation

The compliant version of the 3-RRR (R -revolute joint) spherical parallel mechanism known as "Agile-Eye"is presented. The kinetostatic analysis of this Compliant Spherical Parallel Mechanism (CSPM) is conducted using the Compliance Matrix Method (CMM) evaluating two different types of Rotational Compliant Joints (RCJs) and with three inputs. These independent inputs could be forces or displacements. Expressions that relate the input forces/displacements with the displacement of the moving platform are obtained from the kinetostatic analysis. These expressions are used to obtain the required inputs to perform a rotational trajectory of the moving platform; parasitic displacements are computed during this process. Analytical results are validated through Finite Element Analysis (FEA). Additionally, the CSPM geometric parameters-parasitic displacements relation is characterized. Those parameters resulting with lower parasitic displacements are determined. Finally, expressions from the kinetostatic analysis are corroborated experimentally using input displacements in a manufactured prototype with parameters selected to have reduced parasitic displacements. Results from the FEA-simulations and experimental tests demonstrated that the expressions obtained from the kinetostatic analysis can accurately describe the force-displacement relations of the proposed CSPM.