Modeling and analysing of spring-loaded double parallelogram mechanism using moment balance

Double Parallelogram Lifting Mechanism (DPLM) is a multi-linkage mechanism adopted as the lifting mechanism of the designed robot in this paper. DPLM is designed based on Double Parallelogram Mechanism (DPM), making it a compact and stable multi-linkage mechanism with a low retracted height and a great working height. This paper investigates the condition in which DPLM obtains static equilibrium at any height using Hookean springs and the minimization of the motor's required torque exertion against the gravitational moment of the weight of the mechanism. A mathematical model describing all the factors involved in moment balancing of DPLM is derived and established in MATLAB and is verified through experiments with a virtual prototype conducted in SOLIDWORKS. The obtained results show that the magnitude of the moment exerted by the tension of a spring can be determined not only by its exact installation positions but also by its D value, which is the difference in the distances between the two installation points of a spring and their respective rotation axes. An optimization method based on minimizing the RMSE of the unbalanced moment for DPLM is introduced.