For the workspace optimization of Delta Parallel Robot (DPR), this paper employs Geometric Modeling Kernel (GMK) to construct DPR’s solid workspace model constrained by two categories of angles with non-toroidal boundaries. Leveraging slicing and interpolating techniques, the maximal inscribed regular space within the DPR’s workspace is obtained in conjunction with numerical optimization methods. With the objective of maximizing effective volume utilization (the volume ratio between the prescribed regular space to the DPR’s workspace) and a prescribed regular space dimension, the Hook-Jeeves direct search method is coupled with the Interior-Point method to attain the optimal geometric DPR parameters on the constrained solid model of workspace. The effectiveness of the algorithm is validated through a design case. This numerical optimization methodology possesses generality, intuitiveness, precision, and high efficiency, theoretically applicable to the workspace optimization for other parallel mechanisms.
LiYHuangTChetwyndDG. An approach for smooth trajectory planning of high-speed pick-and-place parallel robots using quintic B-splines. Mech Mach Theory2018; 126: 479–490.
2.
MoustrisGTzafestasC. Modelling and analysis of a parallel double delta mechanism for robotic surgery. In: 30th Mediterranean conference on control and automation (MED), Divani Apollon Palace & Thalasso Athens, Greece, 28 June-1 July 2022, pp.861–866. New York: IEEE.
3.
ChenJSanH. Workspace analysis for a five degrees of freedom hybrid engraving plotter. J Eng2019; 2019: 278–283.
4.
RodriguezERiañoCAlvaresA, et al. Design and dimensional synthesis of a linear delta robot with single legs for additive manufacturing. J Braz Soc Mech Sci2019; 41: 1–23.
5.
MitsantisukCStapornchaisitSNiramitvasuN, et al. Force sensorless control with 3D workspace analysis for haptic devices based on delta robot. In: 41st annual conference of the IEEE industrial electronics society (IECON), Yokohama, Japan, 9−12 November 2015, pp.001747−001752. New York: IEEE.
6.
BrinkerJCorvesBTakedaY. Kinematic performance evaluation of high-speed delta parallel robots based on motion/force transmission indices. Mech Mach Theory2018; 125: 111–125.
7.
SiGChuMZhangZ, et al. Integrating dynamics into design and motion optimization of a 3-PRR planar parallel manipulator with discrete time transfer matrix method. Math Probl Eng2020; 2020: 1–23.
8.
StamperRETsaiLWWalshGC. Optimization of a three DOF translational platform for well-conditioned workspace. In: Proceedings of international conference on robotics and automation (ICRA), Albuquerque, USA, 25 April 1997, pp.3250−3255. New York: IEEE.
9.
StockMMillerK. Optimal kinematic design of spatial parallel manipulators: application to linear delta robot. J Mech Des2003; 125: 292–301.
10.
KhalidAMekidSKhalidA, et al. Intelligent spherical joints based tri-actuated spatial parallel manipulator for precision applications. Robot Comput Integr Manuf2018; 54: 173–184.
11.
GuoWZGaoFMekidS. A new analysis of workspace performances and orientation capability for 3-DOF planar manipulators. Int J Robot Autom2010; 25: 89–101.
12.
KucukS. Simulation and design tool for performance analysis of planar parallel manipulators. Simulation2012; 88: 542–556.
13.
MahmoodiMTabriziMGAlipourK. A new approach for kinematics-based design of 3-RRR delta robots with a specified workspace. In: 2015 AI & robotics (IRANOPEN), Qazvin, Iran, 12 April 2015, pp.1−6. New York: IEEE.
14.
DastjerdiAHSheikhiMMMasoulehMT. A complete analytical solution for the dimensional synthesis of 3-DOF delta parallel robot for a prescribed workspace. Mech Mach Theory2020; 153: 1–18.
15.
LiuXJWangJOhKK, et al. A new approach to the design of a DELTA robot with a desired workspace. J Intell Robot Syst2004; 39: 209–225.
16.
LeHNLeXH. Geometrical design of a RUU type Delta robot based on the predescribed workspace. In: 4th international conference on green technology and sustainable development (GTSD), Ho Chi Minh City, Vietnam, 23−24 November 2018, pp.359−364. New York: IEEE.
17.
AboulissaneBEl BakkaliLEl BahaouiJ. Workspace analysis and optimization of the parallel robots based on computer-aided design approach. FU Mech Eng2020; 18: 079–089.
18.
OarceaAPopisterFStanSD, et al. Comparative study of CAD optimization features for the workspace of 3DOF parallel robot. In: 9th international conference on modern power systems (MPS), Cluj-Napoca, Romania, 16−17 June 2021, pp.1−6. New York: IEEE.
19.
ChaudhuryANGhosalA. Optimum design of multi-degree-of-freedom closed-loop mechanisms and parallel manipulators for a prescribed workspace using Monte Carlo method. Mech Mach Theory2017; 118: 115–138.
20.
EryılmazCOmurluVE. Sqp optimization of 6dof 3x3 upu parallel robotic system for singularity free and maximized reachable workspace. J Robot2019; 2019: 1–14.
21.
KumarPSudheeAP. Workspace optimization of 3PRR parallel manipulator for drilling operation using genetic algorithm. In: Proceedings of the 2017 3rd international conference on advances in robotics (AIR), New Delhi, India, 28 June−2 July 2017, pp.1−5. New York: ACM.
22.
LaribiMARomdhaneLZeghloulS. Analysis and dimensional synthesis of the DELTA robot for a prescribed workspace. Mech Mach Theory2007; 42: 859–870.
23.
FarooqSSBaqaiAAShahMF. Optimal design of tricept parallel manipulator with particle swarm optimization using performance parameters. J Eng Res2021; 9: 2307–1877.
24.
McCormickEWangYLangH. Optimization of a 3-RRR delta robot for a desired workspace with real-time simulation in MATLAB. In: 14th international conference on computer science & education (ICCSE), Toronto, Canada, 19−21 August 2019, pp.935−941. New York: IEEE.
25.
LiuXJWangJ. A new methodology for optimal kinematic design of parallel mechanisms. Mech Mach Theory2007; 42: 1210–1224.
AyizCKucukS. The kinematics of industrial robot manipulators based on the exponential rotational matrices. In: 2009 IEEE international symposium on industrial electronics (ISIE), Seoul, Korea (South), 5−8 July 2009, pp.977−982. New York: IEEE.
30.
KucukS. Maximal dexterous trajectory generation and cubic spline optimization for fully planar parallel manipulators. Comput Electr Eng2016; 56: 634–647.
