EXTENDING THE ADJUSTING KINEMATIC PARAMETER APPROACH TO SPATIAL ROBOTIC MECHANISMS
Date
2019-09-13
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
ORCID
0000-0003-4306-6854
Type
Thesis
Degree Level
Masters
Abstract
Robotic mechanisms refer to mechanisms that include at least one varying speed motor (servomotor). Dynamic balancing is a critical issue in designing robotic mechanisms, which affects their accuracy and efficiency. The force and moment from robotic mechanisms can cause vibration motions on the base, which is called the shaking force and shaking moment (including torque), while at the same time causes “small” vibration motions on the body of the mechanism. Several well-known methods are available for decades for balancing the shaking force and shaking moment, including the counter-weight (CW) method, add-of-spring (AOS) method, add-of-linkage (AOL), and adjusting kinematic parameter (AKP). AKP was developed in our group in 1990s; however, it is only applicable to planar robotic mechanisms.
The primary objective of this thesis was to extend AKP to spatial robotic mechanisms. A spherical parallel robotic mechanism, which is a type of spatial robotic mechanisms, was chosen as a study vehicle due to their relatively simple kinematics and dynamics. The mechanism is symmetrical consisting of three legs and one mobile platform, where the end effector (e.g., camera orienting device) is mounted. Each leg contains a lower link and an upper link. The equations for force balancing using AKP were derived by (1) writing the position vectors of the COM of mechanisms with respect to the reference point ‘O’, (2) writing the expression of the COM into a form that includes the time-dependent term (Bi) and the non time-dependent term (Ai), and (3) letting all Bi be zero, i.e., Bi=0, which are the equations for force balancing. Simulation was performed by the software called SPACAR developed at TU Delft. The simulation results showed the effectiveness of the AKP approach to spatial spherical mechanisms for force balancing.
Another objective of this thesis was to use a combination of AKP and CW to dynamic balance a spherical mechanism. Dynamic balancing includes both force and moment balancing. The condition of moment balancing is that the total angular momentum of the mechanism with respect to a reference point remains zero. The equations for moment balancing were derived with three steps: (1) letting the angular momentum of the mechanism with respect to the center point to zero, which results into an equation; (2) writing this equation into a format that the time-dependent term (Bi) and the term (Ai) that includes the dimension and mass distribution are separate, like A0 + A1B1+A2B2+…+AnBn; (3) letting all Ai be zero. Using SPACAR as the simulation tool, the results again showed the effectiveness of the AKP approach to dynamic balancing for spatial mechanisms.
The final objective was to optimize the mechanism which has been force balanced for the minimal shaking moment; this problem is also called partial shaking moment balancing. The problem was formulated by considering the minimization of shaking moment as an objective function while the force balancing equation as a constraint equation. The variables in the optimization problem are the masses and lengths of the links. The function ‘fmincon’ from the MATLAB optimization toolbox was employed for solving this optimization problem. Using the SPACAR software, a simulation was conducted to show the effectiveness of the approach to partial dynamic balancing of spherical mechanisms.
The main contributions of this thesis lie in the field of balancing of robotic mechanisms. Specifically, the thesis extends the AKP approach to spatial robotic mechanisms, which provides more means to balancing of spatial robotic mechanisms. It is noted that each method has its pros and cons, and a combined use of several methods is a strategy for improvement of the quality of balancing. For the first time, the thesis provides a combined AKP and CW approach to fully dynamic balancing a spatial mechanism. Finally, the thesis demonstrates the feasibility of optimal moment balancing when the mechanism has already been force balanced with the combined AKP and CW approach.
Description
Keywords
dynamic balancing, spatial robotic mechanisms
Citation
Degree
Master of Science (M.Sc.)
Department
Mechanical Engineering
Program
Mechanical Engineering