Analytical Kinematic Modelling and Numerical Cross-Verification of a Planar Linkage Mechanism with Linear Actuation

Space-constrained articulated mechanisms integrated into mechatronic assemblies require rigorous kinematic characterisation during preliminary design, since spatial limitations and the avoidance of kinematic locking in the transient regime constrain the admissible geometry. An original planar guidance-and-retraction linkage is analysed, composed of three fixed joints, a linear hydraulic actuator, a rigid block of six interconnected elements, and two guiding links that suppress the out-of-plane degrees of freedom; the retractable landing gear of a light training aircraft is adopted as the application case. All mobile joints are expressed in closed form as explicit functions of a single input parameter, the actuator length, without decomposition into Assur groups or iterative compatibility equations. The analytical positions, velocities and accelerations were cross-verified against two independent packages, Linkage v.3.16.14 and GIM v.2025.4; deviations remain below 0.25% of the amplitude of each quantity, with velocity root-mean-square deviations below 0.16 mm/s. The guiding dyad reaches neither dead-centre over the stroke, although its link lengths are treated as preliminary because the 35° minimum transmission-angle margin is not maintained over the first 2.2% of the stroke, for which a corrective dimensioning is provided. The closed-form characterisation provides a basis for subsequent structural, dynamic and experimental analysis.