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

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.

Graphical abstract

Keywords

translational parallel mechanism / single loop / multiple driving system / workspace analysis / singularity

References

[1] Stewart D . A platform with six degrees of freedom. Proceedings of the Institution of Mechanical Engineers, 1965, 180(1): 371–386

[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

[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

[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

[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

[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

[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

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

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

[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

[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

[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

[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

[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

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

[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

[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

[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

[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

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

[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

[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

[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

[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

[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

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

[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

[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

[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

[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

Nomenclature

a_1, a_2, a_3	Lengths of links O{A}_{\text{1}}, O{A}_2, and A_{\text{1}}{A}_{\text{3}}, respectively
b_i	Length of link A_i{B}_i (i = 1, 2, 3)
c_i	Length of link B_i{C}_i (i = 1, 2, 3)
{\dot{d}}_{ij}	Intensity associated with the jth prismatic joint in the ith limb (i = 1, 2, and j = 1, 2)
\left\{D\right\}	6-dimensional rigid motion
\left\{G(\mathit{u})\right\}, \left\{G(\mathit{v})\right\}	Planar motion determined by the normal vectors u and v, respectively
\left\{G_2(\mathit{v})\right\}	A subset of \left\{G(\mathit{v})\right\}
h	Distance between point o and the center point of the end effector
k	Nonzero coefficient
l_i	Length of different links
m	Component of distance between points o and C_i in the y-direction (i = 1, 2, 3)
\left\{M\right\}	Displacement submanifold of the terminal body relative to the base body
\left\{M_{\text{S}i}\right\}	Motion subgroup of the ith serial kinematic chain (i = 1, 2)
\left\{M({\mathit{u}}_i)\right\}	Displacement subgroup associated with the ith joint (i = 1, 2, …, n)
n	Component of distance between points o and C_i in the x-direction (i = 1, 2, 3)
\left\{Pa(\mathit{u})\right\}, \left\{Pa(\mathit{v})\right\}, \left\{Pa(\mathit{w})\right\}	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
\left\{R(N,\mathit{u})\right\}, \left\{R(N,\mathit{v})\right\}	Rotations about the axis determined by the point N and the unit vectors u and v, respectively
\left\{R(N_i,\mathit{u})\right\}, \left\{R(N_i,\mathit{v})\right\}, \left\{R(N_i,\mathit{w})\right\}	Rotations about the axis determined by the point N_i and the unit vectors u, v, and w, respectively (i = 1, 2, …, 6)
S_i	ith serial kinematic chain (i = 1, 2)
{\mathit{s}}_{ij}	Unit vector associated with the jth joint of the ith limb (i = 1, 2, and j = 1, 2, …, 4)
{\mathit{s}}_{\text{r}ij}	Unit vector associated with the jth reciprocal wrench in the ith limb (i = 1, 2, and j = 1, 2)
\left\{T\right\}	3-dimensional translation in space
\left\{T(\mathit{u})\right\}, \left\{T(\mathit{v})\right\}, \left\{T(\mathit{w})\right\}	Translations along the unit vectors u, v, and w, respectively
{\mathit{v}}_{\text{p}}^{}	Linear velocity of the center of mass of the mobile platform
{\mathit{w}}_{\text{p}}^{}	Angular velocity of the center of mass of the mobile platform
x_{A\text{1}}	Motion parameter of actuated prismatic pair in the first limb
\left\{X(\mathit{u})\right\}, \left\{X(\mathit{v})\right\}, \left\{X(\mathit{w})\right\}	3-dimensional translation and one rotation about the unit vectors u, v, and w, respectively
y_{A\text{2}}	Motion parameter of actuated prismatic pair in the second limb
\alpha	Output rotational angle around one axis in the 2-DOF driving system
{\alpha }_1	Angle between the Y axis and the long rod of the parallelogram joint in the first limb
{\alpha }_2	Angle between the X axis and the long rod of the parallelogram joint in the second limb
\theta	Output rotational angle around the other axis in the 2-DOF driving system
{\theta }_i	Rotational angles of the first revolute pair in the ith limb (i = 1, 2)
{\dot{\theta }}_{ij}	Intensity associated with the jth revolute joint in the ith limb (i = 1, 2, and j = 1, 2)
{\mathit{\text{\$}}}_{\text{p}}	Instantaneous twist of the end effector
{\mathit{\text{\$}}}_{ij}	Unit screw of the jth joint in the ith limb (i = 1, 2, and j = 1, 2, …, 4)
{\mathit{\text{\$}}}_{\text{r}ij}	jth reciprocal wrench in the ith limb (i = 1, 2, and j = 1, 2)
{\gamma }_i	Rotational angle of the cylindrical joint in the ith limb (i = 1, 2, 3)
{\phi }_i	Angle between links A_i{B}_i and B_i{C}_i (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.

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