# Dynamic Analysis of a Delta Parallel Robot with Flexible Links and Joint Clearances
## 4 Conclusions  
A new approach is employed in this paper by analyzing the impact of three factors on the kinematic and dynamic behavior of the Delta parallel robot: the elasticity of the robot's simple elements (rod elements), friction and clearance in the spherical joints. For this purpose, the analysis was carried out for the case study of a Delta SIAX 3-1600-type robot based on the 3D models developed in CATIA and simulated in the ADAMS software. The following summarizes the effects of these factors' actions on the movement trajectory:  
* Friction has an insignificant influence on the movement parameters of the characteristic point (displacement, speed, acceleration);  
Figure 21: Driving torque deviations in Scenario 7 (red solid line) and the additive effect of clearance, friction and elasticity factors (blue dashed line) for (**a**) arm A; (**b**) arm B and (**c**) arm C.  
Figure 20: Motion deviations in Scenario 7 (red solid line) and the additive effect of friction, elasticity and clearance factors (blue dashed line) for (**a**) displacement; (**b**) velocity and (**c**) acceleration of the characteristic point. The elasticity of the elements causes practically negligible deviations in the displacement on the trajectory (of the order of \(10^{-6}\) m), small deviations on velocity (of the order of \(10^{-4}\) m/s), but significant in the acceleration (of up to 5 m/s\({}^{2}\)); Joint clearances (considered at the value of 0.1 mm) have a substantial effect on the characteristic point displacement (deviations of the order of \(10^{-4}\) m), moderate on velocity (of the order of \(10^{-3}\) m/s) and relatively negligible on acceleration (of order \(10^{-2}\) m/s\({}^{2}\)); The coupling of any two of these factors results in the cumulative effects on kinematics and dynamics, except in Scenario 6, where the deviations reach values three times higher than those in the case of the individual effects summation; The coupling of the three factors leads, from a kinematic point of view, to a slight reduction in deviations, except for acceleration, where a significant reduction in deviations, and especially in picks, can be observed, leading to a better numerical integration solution; Regarding dynamics, the effects of the three factors are the following: Friction in the joints causes a practically insignificant variation in the driving torques (of the order of \(10^{-1}\) N\(\cdot\)m) compared to their nominal values of the order of 103 N\(\cdot\)m (<750 N\(\cdot\)m); The elasticity of the elements has a substantial impact on driving torques (deviations of up to 25 N\(\cdot\)m, i.e., 3.3%, with a harmonic evolution); Joint clearances have a moderate effect on driving torques (<2 N\(\cdot\)m); When two factors are combined (except in Scenario 6), the deviations can reach vaues up to two times higher compared to the case of the summation of individual effects and values up to three times higher when all three factors are combined. For all factor coupling scenarios (S4-S7), the study observed that individual effects are not always cumulative. The coupling of factors can increase deviation values when the clearances and elasticities in the joints are considered simultaneously. Consequently, it is not recommended to simulate these factors separately and sum their effects. Since the phenomena are not linear, a combined approach of the factors is necessary to obtain relevant results. The authors propose to validate the conclusions of this theoretical study resulting from numerical simulations in the ADAMS software through experimental means in the future. Conceptualization, M.N. and N.C.; methodology, N.C., M.N. and R.S. ; software, N.C. and R.S. ; validation, M.N., N.C. and R.S. ; formal analysis, M.N. and N.C.; investigation, N.C. and R.S. ; resources, N.C., M.N. and R.S. ; data curation, M.N. and R.S. ; writing--original draft preparation, N.C.; writing--review and editing, M.N. and R.S; visualization, N.C and R.S. ; supervision, M.N. All authors have read and agreed to the published version of the manuscript.