Journal of Mechanical Science and Technology 35 (4) 2021 DOI 10.1007/s12206-021-0334-5 1711 Journal of Mechanical Science and Technology 35 (4) 2021 Original Article DOI 10.1007/s12206-021-0334-5 Keywords: · Compliant mechanism · Experimental validation · Modeling · Trajectory control Correspondence to: Ayse Tekes atekes@kennesaw.edu Citation: Garcia, M., McFall, K., Tekes, A. (2021). Trajectory control of planar closed chain fully compliant mechanism. Journal of Mechanical Science and Technology 35 (4) (2021) 1711~1719. http://doi.org/10.1007/s12206-021-0334-5 Received March 11th, 2020 Revised December 21st, 2020 Accepted January 12th, 2021 † Recommended by Editor Ja Choon Koo Trajectory control of planar closed chain fully compliant mechanism Martin Garcia 1 , Kevin McFall 2 and Ayse Tekes 1 1 Department of Mechanical Engineering, Kennesaw State University, Marietta, GA 30060, USA, 2 Department of Mechatronics Engineering, Kennesaw State University, Marietta, GA 30060, USA Abstract This study presents the design, analysis, dynamical modeling and control of a planar, flexure based closed chain compliant mechanism. Mechanism is designed as a single piece and comprised of rigid-flexure links connected in series. Base links of the mechanism can be actuated through two servo motors and translated along the horizontal direction using two step motors. Two servo motors are mounted on a rail-cart system and carts are equipped with belt drive to enable horizontal displacement. Dynamical model of the mechanism is derived by adapting pseudo rigid body modeling method, vector closure loop equations, Euler’s laws of motion and geometric constraints. Mechanism is 3D printed using thermoplastic polyurethane filament (TPU), motion of the mechanism is video recorded and position of the tip along with the motion of center of each links are captured using image processing. Mathematical model is simulated in Matlab Simulink and validated with the experimental data. A reference trajectory drawn within the workspace of the mechanism on iPad is successfully traced in real time using the simplified model, mirror imaging program and inverse kinematics. The proposed mecha- nism can be utilized as a haptic device and a compliant manipulator in industrial applications where high precision and larger workspace is desired. 1. Introduction Design and analysis of chain mechanisms is still an active research area as they found broader application from manipulation of diverse objects to assembly where continuous and laborious process is required. Open chain robotic manipulators are commonly preferred for pick and place tasks and demand more actuators and sensors to control the orientations of each link giving rise to the increase of inertia and low performance compared to the closed chain robots. Often actuators are placed at the base links on a closed chain mechanism thereby re- ducing the inertia. However, one drawback of a closed chain is the complexity in the dynamical model rising from the kinematic constraints in comparison with open chain mechanisms [1-4]. Control and analysis of underactuated or fully actuated closed chain mechanisms have well been studied in the Refs. [5-8]. Compliant mechanisms exhibit better performance compared to the traditionally designed rigid mechanisms as they can be designed and manufactured as a single piece without the requirement of any joints; leading to no friction and backlash [9]. How- ever, similar to the closed chain mechanisms, dynamical analysis of compliant mechanisms is challenging as estimating the deflection shape of the flexible links is difficult. Several ap- proaches can be adopted from literature. Elliptic integral method is suitable for compliant mechanisms using simple initially straight flexible links such as in parallel guiding mechanisms [10], folded arm beam [11], dwell [9, 12] and bistable mechanisms [13, 14]. Pseudo rigid body modeling (PRBM) in which the flexible links or flexures are displaced with a torsional spring having the same torsional stiffness provides accurate solution [15]. Alternatively, flexible link can be discretized into small links as in discrete beam element method to find the load- deflection relation at any point or finite element analysis can also be utilized for complex ge- ometries. Closed chain multi-link mechanisms particularly two degrees of freedom (DOF) and planar © The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2021