RESEARCH ARTICLE

Design and analysis of partially decoupled translational parallel mechanisms with single-loop structures

  • Lin WANG 1,2 ,
  • Yuefa FANG , 1 ,
  • Dan ZHANG 2 ,
  • Luquan LI 1
Expand
  • 1. Department of Mechanical Engineering, Beijing Jiaotong University, Beijing 100044, China
  • 2. Department of Mechanical Engineering, Lassonde School of Engineering, York University, Toronto, ON M3J 1P3, Canada

Received date: 14 Dec 2021

Accepted date: 16 Apr 2022

Published date: 15 Sep 2022

Copyright

2022 Higher Education Press

Abstract

This study presents a family of novel translational parallel mechanisms (TPMs) with single-loop topological structures. The proposed mechanism consists of only revolute and prismatic joints. The novel TPMs are simpler in structure and have fewer joints and components than the well-known Delta Robot. Four types of 2-degree of freedom driving systems are applied to different limb structures to avoid the moving actuator that causes the problem of increased moving mass. Four sample TPMs are constructed using the synthesized limbs, and one of them is investigated in terms of kinematic performance. First, a position analysis is performed and validated through numerical simulation to reveal the characteristics of partially decoupled motion, which improves the controllability of TPM. Second, singular configurations are identified, and the resulting singularity curve is obtained. Lastly, the workspace of TPM is analyzed, and the relationship between the singular configurations and the reachable workspace is explored. The workspace of the 3-CRR (C denotes the cylindrical joint and R denotes the revolute joint) translational mechanism is also presented to prove that the proposed TPM has a fairly large workspace.

Cite this article

Lin WANG , Yuefa FANG , Dan ZHANG , Luquan LI . Design and analysis of partially decoupled translational parallel mechanisms with single-loop structures[J]. Frontiers of Mechanical Engineering, 2022 , 17(3) : 39 . DOI: 10.1007/s11465-022-0695-1

Nomenclature

a1, a2, a3Lengths of links OA1, OA2, and A1A3, respectively
biLength of link AiBi (i = 1, 2, 3)
ciLength of link BiCi (i = 1, 2, 3)
d˙ijIntensity associated with the jth prismatic joint in the ith limb (i = 1, 2, and j = 1, 2)
{D}6-dimensional rigid motion
{G(u)}, {G(v)}Planar motion determined by the normal vectors u and v, respectively
{G2(v)}A subset of {G(v)}
hDistance between point o and the center point of the end effector
kNonzero coefficient
liLength of different links
mComponent of distance between points o and Ci in the y-direction (i = 1, 2, 3)
{M}Displacement submanifold of the terminal body relative to the base body
{MSi}Motion subgroup of the ith serial kinematic chain (i = 1, 2)
{M(ui)}Displacement subgroup associated with the ith joint (i = 1, 2, …, n)
nComponent of distance between points o and Ci in the x-direction (i = 1, 2, 3)
{Pa(u)}, {Pa(v)}, {Pa(w)}Translations along the direction perpendicular to the long side of the parallelogram with the axes of revolute joints in the composite joint parallel to the u, v, and w direction, respectively
{R(N,u)}, {R(N,v)}Rotations about the axis determined by the point N and the unit vectors u and v, respectively
{R(Ni,u)}, {R(Ni,v)}, {R(Ni,w)}Rotations about the axis determined by the point Ni and the unit vectors u, v, and w, respectively (i = 1, 2, …, 6)
Siith serial kinematic chain (i = 1, 2)
sijUnit vector associated with the jth joint of the ith limb (i = 1, 2, and j = 1, 2, …, 4)
srijUnit vector associated with the jth reciprocal wrench in the ith limb (i = 1, 2, and j = 1, 2)
{T}3-dimensional translation in space
{T(u)}, {T(v)}, {T(w)}Translations along the unit vectors u, v, and w, respectively
vpLinear velocity of the center of mass of the mobile platform
wpAngular velocity of the center of mass of the mobile platform
xA1Motion parameter of actuated prismatic pair in the first limb
{X(u)}, {X(v)}, {X(w)}3-dimensional translation and one rotation about the unit vectors u, v, and w, respectively
yA2Motion parameter of actuated prismatic pair in the second limb
αOutput rotational angle around one axis in the 2-DOF driving system
α1Angle between the Y axis and the long rod of the parallelogram joint in the first limb
α2Angle between the X axis and the long rod of the parallelogram joint in the second limb
θOutput rotational angle around the other axis in the 2-DOF driving system
θiRotational angles of the first revolute pair in the ith limb (i = 1, 2)
θ˙ijIntensity associated with the jth revolute joint in the ith limb (i = 1, 2, and j = 1, 2)
$pInstantaneous twist of the end effector
$ijUnit screw of the jth joint in the ith limb (i = 1, 2, and j = 1, 2, …, 4)
$rijjth reciprocal wrench in the ith limb (i = 1, 2, and j = 1, 2)
γiRotational angle of the cylindrical joint in the ith limb (i = 1, 2, 3)
φiAngle between links AiBi and BiCi (i = 1, 2, 3)

Acknowledgements

This research work was supported by the Fundamental Research Funds for the Central Universities, China (Grant No. 2020YJS153) and the National Natural Science Foundation of China (Grant No. 51975039). Then, the first author would like to acknowledge the China Scholarship Council (Grant No. 202007090138) for financial support and the use of the research facilities at Lassonde School of Engineering at York University, Canada.
1
Stewart D . A platform with six degrees of freedom. Proceedings of the Institution of Mechanical Engineers, 1965, 180(1): 371–386

DOI

2
St-Onge B M , Gosselin C M . Singularity analysis and representation of the general Gough-Stewart platform. The International Journal of Robotics Research, 2000, 19(3): 271–288

DOI

3
Tong Z Z , Gosselin C , Jiang H Z . Dynamic decoupling analysis and experiment based on a class of modified Gough-Stewart parallel manipulators with line orthogonality. Mechanism and Machine Theory, 2020, 143: 103636

DOI

4
You J J , Xi F F , Shen H P , Wang J Y , Yang X L . A novel Stewart-type parallel mechanism with topological reconfiguration: design, kinematics and stiffness evaluation. Mechanism and Machine Theory, 2021, 162: 104329

DOI

5
Akçali I D , Mutlu H . A novel approach in the direct kinematics of Stewart platform mechanisms with planar platforms. Journal of Mechanical Design, 2006, 128(1): 252–263

DOI

6
Jin X D , Fang Y F , Zhang D , Luo X L . Design and analysis of a class of redundant collaborative manipulators with 2D large rotational angles. Frontiers of Mechanical Engineering, 2020, 15(1): 66–80

DOI

7
Wang L , Fang Y F , Li L Q . Design and analysis of the gripper mechanism based on generalized parallel mechanisms with configurable moving platform. Frontiers of Mechanical Engineering, 2021, 16(4): 765–781

DOI

8
Tian C X , Zhang D . A new family of generalized parallel manipulators with configurable moving platforms. Mechanism and Machine Theory, 2020, 153: 103997

DOI

9
Tian C X , Zhang D . Design and analysis of novel kinematically redundant reconfigurable generalized parallel manipulators. Mechanism and Machine Theory, 2021, 166: 104481

DOI

10
Clavel R . DELTA, a fast robot with parallel geometry. In: Proceedings of the 18th International Symposium on Industrial Robots. New York: Springer, 1988, 91–100

11
Laribi M A , Romdhane L , Zeghloul S . Analysis and dimensional synthesis of the Delta Robot for a prescribed workspace. Mechanism and Machine Theory, 2007, 42(7): 859–870

DOI

12
Dastjerdi A H , Sheikhi M M , Masouleh M T . A complete analytical solution for the dimensional synthesis of 3-DOF Delta parallel robot for a prescribed workspace. Mechanism and Machine Theory, 2020, 153: 103991

DOI

13
Stock M , Miller K . Optimal kinematic design of spatial parallel manipulators: application to linear Delta Robot. Journal of Mechanical Design, 2003, 125(2): 292–301

DOI

14
Liu X J , Wang J S , Oh K K , Kim J W . A new approach to the design of a Delta Robot with a desired workspace. Journal of Intelligent & Robotic Systems, 2004, 39(2): 209–225

DOI

15
Silva V G , Tavakoli M , Marques L . Optimization of a three degrees of freedom Delta manipulator for well-conditioned workspace with a floating point genetic algorithm. International Journal of Natural Computing Research, 2014, 4(4): 1–14

DOI

16
Di Gregorio R . Kinematics of the translational 3-URC mechanism. Journal of Mechanical Design, 2004, 126(6): 1113–1117

DOI

17
Tsai L W , Walsh G C , Stamper R E . Kinematics of a novel three DOF translational platform. In: Proceedings of IEEE International Conference on Robotic and Automation. Minncapolis: IEEE, 1996, 3446–3451

DOI

18
Tsai L W . Kinematics of a three-DOF platform with three extensible limbs. In: Lenarčič J, Parenti-Castelli V, eds. Recent Advances in Robot Kinematics. Dordrecht: Springer, 1996, 401–410

DOI

19
Li Y M , Xu Q S . Kinematic analysis and design of a new 3-DOF translational parallel manipulator. Journal of Mechanical Design, 2006, 128(4): 729–737

DOI

20
Stan S D , Balan R , Maties V , Teutan E , Vlad T . Design and control simulation of ISOGLIDE3 parallel robot. In: Proceedings of the 8th Conference on Applied Informatics and Communications. Rhodes, 2008, 272–275

21
Ganesh S S , Koteswara Rao A B , Darvekar S . Multi-objective optimization of a 3-DOF translational parallel kinematic machine. Journal of Mechanical Science and Technology, 2013, 27(12): 3797–3804

DOI

22
Callegari M , Tarantini M . Kinematic analysis of a novel translational platform. Journal of Mechanical Design, 2003, 125(2): 308–315

DOI

23
Yu W D , Wang H , Chen G L . Design and kinematic analysis of a 3-translational-DOF spatial parallel mechanism based on polyhedral. Mechanism and Machine Theory, 2018, 121: 92–115

DOI

24
Chablat D , Wenger P . Architecture optimization of a 3-DOF translational parallel mechanism for machining applications, the orthoglide. IEEE Transactions on Robotics and Automation, 2003, 19(3): 403–410

DOI

25
Yu J J , Dai J S , Bi S S , Zong G H . Numeration and type synthesis of 3-DOF orthogonal translational parallel manipulators. Progress in Natural Science, 2008, 18(5): 563–574

DOI

26
Shen H P , Chablat D , Zeng B X , Li J , Wu G L , Yang T L . A translational three-degrees-of-freedom parallel mechanism with partial motion decoupling and analytic direct kinematics. Journal of Mechanisms and Robotics, 2020, 12(2): 021112

DOI

27
Zou Q , Zhang D , Luo X L , Huang G Y , Li L J , Zhang H Q . Enumeration and optimum design of a class of translational parallel mechanisms with prismatic and parallellelogram joints. Mechanism and Machine Theory, 2020, 150: 103846

DOI

28
Karimi Eskandary P , Angeles J . The virtual screw: concept, design and applications. Mechanism and Machine Theory, 2018, 128: 349–358

DOI

29
Hervé J M. Structural analysis of mechanisms by displacement group. Mechanism and Machine Theory, 1978, 13(4): 437–450 (in French)

30
Li Q C , Huang Z , Hervé J M . Displacement manifold method for type synthesis of lower-mobility parallel mechanisms. Science in China Series E: Technological Sciences, 2004, 47(6): 641–650

DOI

31
Tsai L W. Robot Analysis: The Mechanics of Serial and Parallel Manipulators. New York: John Wiley & Sons, Inc., 1999

32
Kong X W , Gosselin C M . Kinematics and singularity analysis of a novel type of 3-CRR 3-DOF translational parallel manipulator. The International Journal of Robotics Research, 2002, 21(9): 791–798

DOI

33
Liu Z H , Niu J C , Zhou Y Q . Kinematics and singularity analysis of 3-CRR parallel mechanism. Journal of Central South University (Science and Technology), 2017, 48(5): 1190–1197

DOI

34
Rodriguez-Leal E , Dai J S , Pennock G R . Screw-system-based mobility analysis of a family of fully translational parallel manipulators. Mathematical Problems in Engineering, 2013, 2013: 262801

DOI

Outlines

/