This article presents a parallel mechanism (PM) that is consists of a UPU and two RPU limbs (U, P, R denote universal joint, prismatic joint, and revolute joint, respectively). It can switch into two different configurations with three degrees of freedom (DOFs), in which one configuration outputs two rotations and one translation, and the other outputs two translations and one rotation. Four joints should be actuated to fully control the PM. Inverse position analysis is carried out. Taking the compliances of links into consideration, wrench analysis of the RU chain is conducted by using screw theory. Stiffness matrix and compliance matrix of the limb are derived through the strain energy method. The PM’s overall stiffness matrix is then obtained according to the deformation compatibility equations. The theoretical results are compared with simulation results obtained in ANSYS, which shows a maximum deviation less than 0.6%. Static stiffness performance evaluation is carried out using the virtual work stiffness index. Performance distributions of the PM in two operation modes under external loads are obtained. The proposed stiffness modeling and performance evaluation could be helpful for optimal design and application investigation of the PM.
GanDDaiJS. Reconfigurable parallel mechanisms: a classification and review. In: Proceedings of the 5th IEEE/IFToMM international conference on reconfigurable mechanisms and robots. ReMAR2021, 2021, p.63.
2.
KongXGosselinCMRichardPL. Type synthesis of parallel mechanisms with multiple operation modes. J Mech Des2007; 129(6): 595–601.
3.
KongX. Type synthesis of 3-DOF parallel manipulators with both a planar operation mode and a spatial translational operation mode1. J Mech Robot2013; 5(4): 041015.
4.
YeWHuLLiQ. Kinematic analysis and dimension optimization of a new reconfigurable parallel mechanism with 1R2T and 2R1T operation modes. J Mech Robot2022; 14(6): 060914.
5.
LiuWLiuH. Synthesis of asymmetric parallel mechanism with multiple 3-DOF motion modes. Adv Mech Eng2022; 14(2): 1–18.
6.
LiuYLiYYaoYA, et al. Type synthesis of multi-mode mobile parallel mechanisms based on refined virtual chain approach. Mech Mach Theory2020; 152: 103908.
7.
NurahmiLCaroSWengerP, et al. Reconfiguration analysis of a 4-RUU parallel manipulator. Mech Mach Theory2016; 96: 269–289.
8.
FanghellaPGallettiCGiannottiE. Parallel robots that change their group of motion. In: LennarčičJRothB (eds) Advances in robot kinematics. Dordrecht: Springer, 2006, pp.49–56.
LiQHervéJM. Parallel mechanisms with bifurcation of Schoenflies motion. IEEE Trans Robot2009; 25(1): 158–164.
11.
WeiJDaiJS. Lie group based type synthesis using transformation configuration space for reconfigurable parallel mechanisms with bifurcation between spherical motion and planar motion. J Mech Des2020; 142(6): 063302.
NurahmiLGanD. Reconfiguration of a 3-(rR)PS metamorphic parallel mechanism based on complete workspace and operation mode analysis. J Mech Robot2020; 12(1): 1–23.
17.
GanDDiasJSeneviratneL. Unified kinematics and optimal design of a 3rRPS metamorphic parallel mechanism with a reconfigurable revolute joint. Mech Mach Theory2016; 96: 239–254.
18.
LiDJiaPLiJ, et al. Constraint and mobility change analysis of Rubik’s cube-inspired reconfigurable joints and corresponding parallel mechanisms. Chin J Mech Eng2020; 33(1): 1–11.
19.
ZhangKDaiJSFangY. Topology and constraint analysis of phase change in the metamorphic chain and its evolved mechanism. J Mech Des2010; 132(12): 121001.
20.
ZhangKDaiJSFangY. Geometric constraint and mobility variation of two 3SvPSv metamorphic parallel mechanisms. J Mech Des2013; 135(1): 011001.
21.
YeWChaiXZhangK. Kinematic modeling and optimization of a new reconfigurable parallel mechanism. Mech Mach Theory2020; 149: 103850.
22.
ChablatDJhaRCaroS. A framework for the control of a parallel manipulator with several actuation modes. In: 2016 IEEE 14th international conference on industrial informatics (INDIN), 2016, pp.190–195. New York, NY: IEEE.
23.
TianYZhangDYaoYA, et al. A reconfigurable multi-mode mobile parallel robot. Mech Mach Theory2017; 111: 39–65.
24.
MoosavianAXiF J. Design and analysis of reconfigurable parallel robots with enhanced stiffness. Mech Mach Theory2014; 77: 92–110.
25.
YouJXiFShenH, et al. A novel Stewart-type parallel mechanism with topological reconfiguration: design, kinematics and stiffness evaluation. Mech Mach Theory2021; 162: 104329.
26.
RongYZhangXCQuMK. Unified inverse dynamics for a novel class of metamorphic parallel mechanisms. Appl Math Model2019; 74: 280–300.
27.
ChablatDKongXZhangC. Kinematics, workspace, and singularity analysis of a parallel robot with five operation modes. J Mech Robot2018; 10(3): 035001.
28.
LiRZhaoJFanD, et al. Design and workspace analysis of reconfigurable 3-RPRP spherical parallel mechanisms. In: 2018 International conference on reconfigurable mechanisms and robots (ReMAR), 2018, pp.1–8. New York, NY: IEEE.
29.
LiDGuoSQuH. A novel multiple working modes parallel mechanism with variable workspace. Proc IMechE, Part C: J Mechanical Engineering Science2020; 234(1): 211–224.
30.
IbarrecheJIHernándezAPetuyaV, et al. A methodology to achieve the set of operation modes of reconfigurable parallel manipulators. Meccanica2019; 54(15): 2507–2520.
31.
El-KhasawnehBSFerreiraPM. Computation of stiffness and stiffness bounds for parallel link manipulators. Int J Mach Tools Manuf1999; 39(2): 321–342.
32.
HuangTZhaoXWhitehouseDJ. Stiffness estimation of a tripod-based parallel kinematic machine. IEEE Trans Robot Autom2002; 18(1): 50–58.
YuGWangLWuJ, et al. Stiffness modeling approach for a 3-DOF parallel manipulator with consideration of nonlinear joint stiffness. Mech Mach Theory2018; 123: 137–152.
35.
GosselinC. Stiffness mapping for parallel manipulators. IEEE Trans Robot Autom1990; 6(3): 377–382.
36.
WenHCongMZhangZ, et al. A redundantly actuated chewing robot based on human musculoskeletal biomechanics: differential kinematics, stiffness analysis, driving force optimization and experiment. Machines2021; 9(8): 171.
37.
YanSJOngSKNeeAYC, et al. Stiffness analysis of parallelogram-type parallel manipulators using a strain energy method. Robot Comput Integr Manuf2016; 37: 13–22.
38.
YangCLiQChenQ, et al. Elastostatic stiffness modeling of overconstrained parallel manipulators. Mech Mach Theory2018; 122: 58–74.
39.
MartinHC. Introduction to matrix methods of structural analysis. New York, NY: McGraw-Hill, 1966.
40.
LiQXuLChenQ, et al. Analytical elastostatic stiffness modeling of overconstrained parallel manipulators using geometric algebra and strain energy. J Mech Robot2019; 11(3): 031007.
41.
HuBHuangZ. Kinetostatic model of overconstrained lower mobility parallel manipulators. Nonlinear Dyn2016; 86(1): 309–322.
42.
ChenGWangHLinZ, et al. The principal axes decomposition of spatial stiffness matrices. IEEE Trans Robot2015; 31(1): 191–207.
43.
WangHZhangLChenG, et al. Parameter optimization of heavy-load parallel manipulator by introducing stiffness distribution evaluation index. Mech Mach Theory2017; 108: 244–259.
44.
LiCGuXXiaoX, et al. Flexible robot with variable stiffness in transoral surgery. IEEE/ASME Trans Mechatron2020; 25(1): 1–10.
45.
YangCLiQChenQ. Decoupled elastostatic stiffness modeling of parallel manipulators based on the rigidity principle. Mech Mach Theory2020; 145: 103718.
46.
GörgülüİDedeMİC. A new stiffness performance index: volumetric isotropy index. Machines2019; 7(2): 44.
47.
HuangZLiQC. Type synthesis of symmetrical lower-mobility parallel mechanisms using the constraint-synthesis method. Int J Rob Res2003; 22(1): 59–79.
