Design and modeling of continuum robot based on virtual-center of motion mechanism

doi:10.1007/s11465-022-0739-6

Frontiers of Mechanical Engineering

2023, Vol. 18

Issue (2): 23 https://doi.org/10.1007/s11465-022-0739-6

本期目录

Design and modeling of continuum robot based on virtual-center of motion mechanism

Guoxin LI¹, Jingjun YU¹, Yichao TANG², Jie PAN¹, Shengge CAO¹, Xu PEI¹(

)

¹. School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China
². Beijing Special Engineering Design and Research Institute, Beijing 100143, China

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Abstract：

Continuum robot has attracted extensive attention since its emergence. It has multi-degree of freedom and high compliance, which give it significant advantages when traveling and operating in narrow spaces. The flexural virtual-center of motion (VCM) mechanism can be machined integrally, and this way eliminates the assembly between joints. Thus, it is well suited for use as a continuum robot joint. Therefore, a design method for continuum robots based on the VCM mechanism is proposed in this study. First, a novel VCM mechanism is formed using a double leaf-type isosceles-trapezoidal flexural pivot (D-LITFP), which is composed of a series of superimposed LITFPs, to enlarge its stroke. Then, the pseudo-rigid body (PRB) model of the leaf is extended to the VCM mechanism, and the stiffness and stroke of the D-LITFP are modeled. Second, the VCM mechanism is combined to form a flexural joint suitable for the continuum robot. Finally, experiments and simulations are used to validate the accuracy and validity of the PRB model by analyzing the performance (stiffness and stroke) of the VCM mechanism. Furthermore, the motion performance of the designed continuum robot is evaluated. Results show that the maximum stroke of the VCM mechanism is approximately 14.2°, the axial compressive strength is approximately 1915 N/mm, and the repeatable positioning accuracies of the continuum robot is approximately ±1.47° (bending angle) and ±2.46° (bending direction).

Key words： VCM mechanism continuum robot flexural joint pseudo-rigid body model cable-driven

收稿日期: 2022-05-10 出版日期: 2023-05-12

Corresponding Author(s): Xu PEI

引用本文:

. [J]. Frontiers of Mechanical Engineering, 2023, 18(2): 23.
Guoxin LI, Jingjun YU, Yichao TANG, Jie PAN, Shengge CAO, Xu PEI. Design and modeling of continuum robot based on virtual-center of motion mechanism. Front. Mech. Eng., 2023, 18(2): 23.

链接本文:

https://academic.hep.com.cn/fme/CN/10.1007/s11465-022-0739-6
https://academic.hep.com.cn/fme/CN/Y2023/V18/I2/23

Fig.1

Fig.2

Fig.3

Tab.1

Tab.2

Fig.4

Symbol	Description
$l single (i)$	Driving cable length in half joint
$Δ l single (i)$	Difference in driving cable length in half joint
$l joint (i)$	Driving cable length in single joint
$Δ l joint (i)$	Difference in driving cable length in single joint
$l segment (i)$	Driving cable length in a single segment
$Δ l segment (i)$	Difference in driving cable length in a single segment
$l total (i)$	Driving cable length of the whole continuum robot
$Δ l total (i)$	Difference in driving cable length of the whole continuum robot
$φ$	Bending angle of the half joint
$θ j o i n t$ , $η j o i n t$	Bending angle and bending direction of the single joint
$θ s e g m e n t$ , $η s e g m e n t$	Bending angle and bending direction of the single segment
$T s e g m e n t$	Pose transformation matrix of the single segment
$T t o t a l$	End pose transformation matrix of the whole continuum robot

Tab.3

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Tab.4

Fig.12

Fig.13

Fig.14

Tab.5

Fig.15

Abbreviations
Al alloy	Aluminum alloy
CLITFP	Compressed leaf-type isosceles-trapezoidal flexural pivot
D-LITFP	Double leaf-type isosceles-trapezoidal flexural pivot
FEA	Finite element analysis
ICR	Instantaneous center of rotation
IE	Intermediate element
LITFP	Leaf-type isosceles-trapezoidal flexural pivot
ME	Movement element
PLA	Polylactic acid
PRB	Pseudo-rigid body
S	Stand
TLITFP	Tensioned leaf-type isosceles-trapezoidal flexural pivot
VCM	Virtual-center of motion
Variables
a₁, a₂	X-coordinate of the end points B and C of link BC
b	Width of the leaf
$C C ′ ¯, D D ′ ¯$	Displacements of points C and D, respectively
E	Elastic modulus
I, I_i	Moments of inertia of the leaf and LITFP i, respectively
F	Force
$F C x$ , $F C y$	Component forces at point C on the X- and Y-axis, respectively
$F D x$ , $F D y$	Component forces at point D on the X- and Y-axis, respectively
$F N C$ , $F N D$	Axial forces applied to link DC on points C and D, respectively
F_RC, F_RD	Radial forces exerted by link BC and AD on points C and D of link DC, respectively
h_f	Height of the lower plane of LITFP from the ICR
h_fi	Height of the lower plane of LITFP i from the ICR, i = 1, 2
H	Height of the upper plane of LITFP from the ICR
H_i	Height of the upper plane of LITFP i from the ICR, i = 1, 2
K	Bending stiffness of LITFP
K_BC, K_AD	Bending stiffness of links BC and AD, respectively
K_d	Bending stiffness of the D-LITFP
K_i	Bending stiffness of the LITFP i, i = 1, 2
K_V	Bending stiffness of the VCM mechanism
$l j o i n t (i)$	Driving cable length in single joint
l_r	Length of the rigid links $A ′ D$ and $B ′ C$
$l s e g m e n t (i)$	Driving cable length in a single segment
$l s i n g l e (i)$	Driving cable length in half joint
$l t o t a l (i)$	Driving cable length of the whole continuum robot
M	A pure bending moment
$M max$	Maximum bending moment which LITFP can bear
n	Position coefficient of ICR
n_i	Position coefficient of the ICR of the LITFP i
r	Radius of the circle where the driving cable is located
$r f$	Result of FEA
$r p$	Calculation result of the PRB model
R	Bending radius
$R b e n d$	Bending radius of the segment
$R Y$	Rotation matrix around the Y-axis
$R Z$	Rotation matrix around the Z-axis
$04 R$ , $04 P$	Rotation matrix and displacement vector from ${O 4}$ to ${O 0}$ , respectively
S_y	Tensile yield strength
t	Thickness of the leaf
t_i	Thickness of the leaf of LITFP i
$T s e g m e n t$	Pose transformation matrix of the single segment
$T t o t a l$	End pose transformation matrix of the whole continuum robot
$01 T$	Coordinate transformation matrix from ${O 1}$ to ${O 0}$
$02 T$	Coordinate transformation matrix from ${O 2}$ to ${O 0}$
$12 T$	Coordinate transformation matrix from ${O 2}$ to ${O 1}$
$α 1$ , $α 2$	Bending angles of link BC and AD under the action of bending moment M
$σ 1 max$ , $σ 2 max$	Maximum stress values corresponding to rotation angles of LITFPs 1 and 2, respectively
σ_dmax, σ_max	Maximum stress of the D-LITFP and LITFP, respectively
$φ$	Bending angle of the half joint
φ_i	Half of the angle between the two leaves of the LITFP i, i = 1, 2
$φ X$ , $φ Y$	X- and Y-axis tilt angles, respectively
θ	Rotation angle (stroke) of the VCM mechanism
$θ d$	Rotation angle of the whole D-LITFP
$θ d max$	Maximum bending angle of the whole D-LITFP
θ_i, θ_imax	(Maximum) Bending angle of the LITFP i, i = 1, 2
$θ j o i n t$ , $θ s e g m e n t$	Bending angles of the single joint and single segment, respectively
θ_max	Maximum bending angle of the LITFP
$η$	Bending direction
$η j o i n t$ , $η s e g m e n t$	Bending directions of the single joint and single segment, respectively
$ε$	Relative error of PRB model with respect to FEA
$Δ l$	Displacement of the force sensor
$Δ l (i)$	Cable length difference
$Δ l j o i n t (i)$	Difference in driving cable length in a single joint
$Δ l s e g m e n t (i)$	Difference in driving cable length in a single segment
$Δ l s i n g l e (i)$	Difference in driving cable length in half joint
$Δ l t o t a l (i)$	Difference in driving cable length of the whole continuum robot

1	F Qi, B Chen, S Y Gao, S G She. Dynamic model and control for a cable-driven continuum manipulator used for minimally invasive surgery. The International Journal of Medical Robotics and Computer Assisted Surgery, 2021, 17(3): e2234 https://doi.org/10.1002/rcs.2234
2	O M Omisore, S P Han, J Xiong, H Li, Z Li, L Wang. A review on flexible robotic systems for minimally invasive surgery. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2022, 52(1): 631–644 https://doi.org/10.1109/TSMC.2020.3026174
3	T L Thomas, V Kalpathy Venkiteswaran, G K Ananthasuresh, S Misra. Surgical applications of compliant mechanisms: a review. Journal of Mechanisms and Robotics, 2021, 13(2): 020801 https://doi.org/10.1115/1.4049491
4	D Axinte, X Dong, D Palmer, A Rushworth, S C Guzman, A Olarra, I Arizaga, E Gomez-Acedo, K Txoperena, K Pfeiffer, F Messmer, M Gruhler, J Kell. MiRoR-miniaturized robotic systems for holistic in-situ repair and maintenance works in restrained and hazardous environments. IEEE/ASME Transactions on Mechatronics, 2018, 23(2): 978–981 https://doi.org/10.1109/TMECH.2018.2800285
5	X Dong, D Axinte, D Palmer, S Cobos, M Raffles, A Rabani, J Kell. Development of a slender continuum robotic system for on-wing inspection/repair of gas turbine engines. Robotics and Computer-Integrated Manufacturing, 2017, 44: 218–229 https://doi.org/10.1016/j.rcim.2016.09.004
6	R Buckingham, A Graham. Nuclear snake-arm robots. Industrial Robot, 2012, 39(1): 6–11 https://doi.org/10.1108/01439911211192448
7	R Buckingham, A Graham. Snaking around in a nuclear jungle. Industrial Robot, 2005, 32(2): 120–127 https://doi.org/10.1108/01439910510582246
8	D Nahar, P M Yanik, I D Walker. Robot tendrils: long, thin continuum robots for inspection in space operations. In: Proceedings of 2017 IEEE Aerospace Conference. Big Sky: IEEE, 2017, 1–8 https://doi.org/10.1109/AERO.2017.7943940
9	P Liljebäck, R Mills. Eelume: a flexible and subsea resident IMR vehicle. In: Proceedings of Oceans 2017-Aberdeen Conference. Aberdeen: IEEE, 2017, 1–4 https://doi.org/10.1109/OCEANSE.2017.8084826
10	Y Yamauchi, Y Ambe, H Nagano, M Konyo, Y Bando, E Ito, S Arnold, K Yamazaki, K Itoyama, T Okatani, H G Okuno, S Tadokoro. Development of a continuum robot enhanced with distributed sensors for search and rescue. Robomech Journal, 2022, 9(1): 8 https://doi.org/10.1186/s40648-022-00223-x
11	M Russo, N Sriratanasak, W M Ba, X Dong, A Mohammad, D Axinte. Cooperative continuum robots: enhancing individual continuum arms by reconfiguring into a parallel manipulator. IEEE Robotics and Automation Letters, 2022, 7(2): 1558–1565 https://doi.org/10.1109/LRA.2021.3139371
12	M F Wang, X Dong, W M Ba, A Mohammad, D Axinte, A Norton. Design, modelling and validation of a novel extra slender continuum robot for in-situ inspection and repair in aeroengine. Robotics and Computer-Integrated Manufacturing, 2021, 67: 102054 https://doi.org/10.1016/j.rcim.2020.102054
13	K P Deashapriya, P A G Sampath, W M S B Wijekoon, N D Jayaweera, A L Kulasekera. Biomimetic flexible robot arm design and kinematic analysis of a novel flexible robot arm. In: Proceedings of 2016 Moratuwa Engineering Research Conference (MERCon). Moratuwa: IEEE, 2016, 385–390
14	Z Li, R X Du. Design and analysis of a bio-inspired wire-driven multi-section flexible robot. International Journal of Advanced Robotic Systems, 2013, 10(4): 209 https://doi.org/10.5772/56025
15	R Buckingham, V Chitrakaran, R Conkie, G Ferguson, A Graham, A Lazell, M Lichon, N Parry, F Pollard, A Kayani, M Redman, M Summers, B Green. Snake-Arm Robots: A New Approach to Aircraft Assembly. SAE International 2007-01-3870, 2007, https://doi.org/10.4271/2007-01-3870
16	P Guardiani, D Ludovico, A Pistone, H Abidi, I Zaplana, J Lee, D G Caldwell, C Canali. Design and analysis of a fully actuated cable-driven joint for hyper-redundant robots with optimal cable routing. Journal of Mechanisms and Robotics, 2022, 14(2): 021006 https://doi.org/10.1115/1.4052332
17	S Bamoriya, C S Kumar. Kinematics of three segment continuum robot for surgical application. In: Kumar R, Chauhan V S, Talha M, Pathak H, eds. Machines, Mechanism and Robotics. Singapore: Springer, 2022, 1011–1021
18	Y Kim, S S Cheng, M Diakite, R P Gullapalli, J M Simard, J P Desai. Toward the development of a flexible mesoscale MRI-compatible neurosurgical continuum robot. IEEE Transactions on Robotics, 2017, 33(6): 1386–1397 https://doi.org/10.1109/TRO.2017.2719035
19	M De Volder, A J M Moers, D Reynaerts. Fabrication and control of miniature McKibben actuators. Sensors and Actuators A: Physical, 2011, 166(1): 111–116 https://doi.org/10.1016/j.sna.2011.01.002
20	G Böttcher, S Lilge, J Burgner-Kahrs. Design of a reconfigurable parallel continuum robot with tendon-actuated kinematic chains. IEEE Robotics and Automation Letters, 2021, 6(2): 1272–1279 https://doi.org/10.1109/LRA.2021.3057557
21	C H Yang, S N Geng, I Walker, D T Branson, J G Liu, J S Dai, R J Kang. Geometric constraint-based modeling and analysis of a novel continuum robot with shape memory alloy initiated variable stiffness. The International Journal of Robotics Research, 2020, 39(14): 1620–1634 https://doi.org/10.1177/0278364920913929
22	Y Chitalia, S Jeong, K K Yamamoto, J J Chern, J P Desai. Modeling and control of a 2-DoF meso-scale continuum robotic tool for pediatric neurosurgery. IEEE Transactions on Robotics, 2021, 37(2): 520–531 https://doi.org/10.1109/TRO.2020.3031270
23	S Park, J Kim, C Kim, K J Cho, G Noh. Design optimization of asymmetric patterns for variable stiffness of continuum tubular robots. IEEE Transactions on Industrial Electronics, 2022, 69(8): 8190–8200 https://doi.org/10.1109/TIE.2021.3104604
24	K Oliver-Butler, J A Childs, A Daniel, D C Rucker. Concentric push-pull robots: planar modeling and design. IEEE Transactions on Robotics, 2022, 38(2): 1186–1200 https://doi.org/10.1109/TRO.2021.3104249
25	C Girerd, T K Morimoto. Design and control of a hand-held concentric tube robot for minimally invasive surgery. IEEE Transactions on Robotics, 2021, 37(4): 1022–1038 https://doi.org/10.1109/TRO.2020.3043668
26	C Rucker, J Childs, P Molaei, H B Gilbert. Transverse anisotropy stabilizes concentric tube robots. IEEE Robotics and Automation Letters, 2022, 7(2): 2407–2414 https://doi.org/10.1109/LRA.2022.3140441
27	K Lee, Y Z Wang, C Q Zheng. Twister hand: underactuated robotic gripper inspired by origami twisted tower. IEEE Transactions on Robotics, 2020, 36(2): 488–500 https://doi.org/10.1109/TRO.2019.2956870
28	J Santoso, C D Onal. An origami continuum robot capable of precise motion through torsionally stiff body and smooth inverse kinematics. Soft Robotics, 2021, 8(4): 371–386 https://doi.org/10.1089/soro.2020.0026
29	S Wu, Q J Ze, J Z Dai, N Udipi, G H Paulino, R K Zhao. Stretchable origami robotic arm with omnidirectional bending and twisting. Proceedings of the National Academy of Sciences of the United States of America, 2021, 118(36): e2110023118 https://doi.org/10.1073/pnas.2110023118
30	B Kang, R Kojcev, E Sinibaldi. The first interlaced continuum robot, devised to intrinsically follow the leader. PLoS One, 2016, 11(2): e0150278 https://doi.org/10.1371/journal.pone.0150278
31	E W Hawkes, L H Blumenschein, J D Greer, A M Okamura. A soft robot that navigates its environment through growth. Science Robotics, 2017, 2(8): eaan3028 https://doi.org/10.1126/scirobotics.aan3028
32	A Sadeghi, E Del Dottore, A Mondini, B Mazzolai. Passive morphological adaptation for obstacle avoidance in a self-growing robot produced by additive manufacturing. Soft Robotics, 2020, 7(1): 85–94 https://doi.org/10.1089/soro.2019.0025
33	S Awtar, A H Slocum. Constraint-based design of parallel kinematic XY flexure mechanisms. Journal of Mechanical Design, 2007, 129(8): 816–830 https://doi.org/10.1115/1.2735342
34	L L Howell, A Midha. A method for the design of compliant mechanisms with small-length flexural pivots. Journal of Mechanical Design, 1994, 116(1): 280–290 https://doi.org/10.1115/1.2919359
35	Z Y Ping, T C Zhang, L Gong, C Zhang, S Y Zuo. Miniature flexible instrument with fibre bragg grating-based triaxial force sensing for intraoperative gastric endomicroscopy. Annals of Biomedical Engineering, 2021, 49(9): 2323–2336 https://doi.org/10.1007/s10439-021-02781-4
36	X Y Wei, Y X Zhang, F Ju, H Guo, B Chen, H T Wu. Design and analysis of a continuum robot for transnasal skull base surgery. The International Journal of Medical Robotics and Computer Assisted Surgery, 2021, 17(6): e2328 https://doi.org/10.1002/rcs.2328
37	H D Wang, X L Wang, W L Yang, Z J Du. Design and kinematic modeling of a notch continuum manipulator for laryngeal surgery. International Journal of Control, Automation, and Systems, 2020, 18(11): 2966–2973 https://doi.org/10.1007/s12555-019-1007-3
38	T Kato, I Okumura, H Kose, K Takagi, N Hata. Tendon-driven continuum robot for neuroendoscopy: validation of extended kinematic mapping for hysteresis operation. International Journal of Computer Assisted Radiology and Surgery, 2016, 11(4): 589–602 https://doi.org/10.1007/s11548-015-1310-2
39	J W Tian, T M Wang, X Fang, Z Y Shi. Design, fabrication and modeling analysis of a spiral support structure with superelastic Ni-Ti shape memory alloy for continuum robot. Smart Materials and Structures, 2020, 29(4): 045007 https://doi.org/10.1088/1361-665X/ab72eb
40	X Pei, J J Yu, G H Zong, S S Bi. An effective pseudo-rigid-body method for beam-based compliant mechanisms. Precision Engineering, 2010, 34(3): 634–639 https://doi.org/10.1016/j.precisioneng.2009.10.001

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