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).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
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
- a 1, a 2 :
-
X-coordinate of the end points B and C of link BC
- b :
-
Width of the leaf
- \(\overline {C{C^\prime}} ,\,\,\overline {D{D^\prime}}\) :
-
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 Cx, F Cy :
-
Component forces at point C on the X- and Y-axis, respectively
- F Dx, F Dy :
-
Component forces at point D on the X- and Y-axis, respectively
- F NC, F ND :
-
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 joint (i):
-
Driving cable length in single joint
- l r :
-
Length of the rigid links A′D and B′C
- l segment (i):
-
Driving cable length in a single segment
- l single (i):
-
Driving cable length in half joint
- l total (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 bend :
-
Bending radius of the segment
- R Y :
-
Rotation matrix around the Y-axis
- R Z :
-
Rotation matrix around the Z-axis
- 40 R, 40 P :
-
Rotation matrix and displacement vector from {O4} to {O0}, respectively
- S y :
-
Tensile yield strength
- t :
-
Thickness of the leaf
- t i :
-
Thickness of the leaf of LITFP i
- T segment :
-
Pose transformation matrix of the single segment
- T total :
-
End pose transformation matrix of the whole continuum robot
- 10 T :
-
Coordinate transformation matrix from {O1} to {O0}
- 20 T :
-
Coordinate transformation matrix from {O2} to {O0}
- 21 T :
-
Coordinate transformation matrix from {O2} to {O1}
- α 1, α 2 :
-
Bending angles of link BC and AD under the action of bending moment M
- σ 1max, σ 2max :
-
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
- σ :
-
Bending angle of the half joint
- σ 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 dmax :
-
Maximum bending angle of the whole D-LITFP
- θ i, θ imax :
-
(Maximum) Bending angle of the LITFP i, i = 1, 2
- θ joint, θ segment :
-
Bending angles of the single joint and single segment, respectively
- θ max :
-
Maximum bending angle of the LITFP
- η :
-
Bending direction
- η joint, η segment :
-
Bending directions of the single joint and single segment, respectively
- ε :
-
Relative error of PRB model with respect to FEA
- Δl :
-
Displacement of the force sensor
- Δl(i):
-
Cable length difference
- Δl joint(i):
-
Difference in driving cable length in a single joint
- Δl segment(i):
-
Difference in driving cable length in a single segment
- Δl single(i):
-
Difference in driving cable length in half joint
- Δl total(i):
-
Difference in driving cable length of the whole continuum robot
References
Qi F, Chen B, Gao S Y, She S G. 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
Omisore O M, Han S P, Xiong J, Li H, Li Z, Wang L. A review on flexible robotic systems for minimally invasive surgery. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2022, 52(1): 631–644
Thomas T L, Kalpathy Venkiteswaran V, Ananthasuresh G K, Misra S. Surgical applications of compliant mechanisms: a review. Journal of Mechanisms and Robotics, 2021, 13(2): 020801
Axinte D, Dong X, Palmer D, Rushworth A, Guzman S C, Olarra A, Arizaga I, Gomez-Acedo E, Txoperena K, Pfeiffer K, Messmer F, Gruhler M, Kell J. 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
Dong X, Axinte D, Palmer D, Cobos S, Raffles M, Rabani A, Kell J. 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
Buckingham R, Graham A. Nuclear snake-arm robots. Industrial Robot, 2012, 39(1): 6–11
Buckingham R, Graham A. Snaking around in a nuclear jungle. Industrial Robot, 2005, 32(2): 120–127
Nahar D, Yanik P M, Walker I D. Robot tendrils: long, thin continuum robots for inspection in space operations. In: Proceedings of 2017 IEEE Aerospace Conference. Big Sky: IEEE, 2017, 1–8
Liljebäck P, Mills R. Eelume: a flexible and subsea resident IMR vehicle. In: Proceedings of Oceans 2017-Aberdeen Conference. Aberdeen: IEEE, 2017, 1–4
Yamauchi Y, Ambe Y, Nagano H, Konyo M, Bando Y, Ito E, Arnold S, Yamazaki K, Itoyama K, Okatani T, Okuno H G, and Tadokoro S. Development of a continuum robot enhanced with distributed sensors for search and rescue. Robomech Journal, 2022, 9(1): 8
Russo M, Sriratanasak N, Ba W M, Dong X, Mohammad A, Axinte D. Cooperative continuum robots: enhancing individual continuum arms by reconfiguring into a parallel manipulator. IEEE Robotics and Automation Letters, 2022, 7(2): 1558–1565
Wang M F, Dong X, Ba W M, Mohammad A, Axinte D, Norton A. 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
Deashapriya K P, Sampath P A G, Wijekoon W M S B, Jayaweera N D, Kulasekera A L. 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
Li Z, Du R X. Design and analysis of a bio-inspired wire-driven multi-section flexible robot. International Journal of Advanced Robotic Systems, 2013, 10(4): 209
Buckingham R, Chitrakaran V, Conkie R, Ferguson G, Graham A, Lazell A, Lichon M, Parry N, Pollard F, Kayani A, Redman M, Summers M, Green B. Snake-Arm Robots: A New Approach to Aircraft Assembly. SAE International 2007-01-3870, 2007
Guardiani P, Ludovico D, Pistone A, Abidi H, Zaplana I, Lee J, Caldwell D G, Canali C. 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
Bamoriya S, Kumar C S. 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
Kim Y, Cheng S S, Diakite M, Gullapalli R P, Simard J M, Desai J P. Toward the development of a flexible mesoscale MRI-compatible neurosurgical continuum robot. IEEE Transactions on Robotics, 2017, 33(6): 1386–1397
De Volder M, Moers A J M, Reynaerts D. Fabrication and control of miniature McKibben actuators. Sensors and Actuators A: Physical, 2011, 166(1): 111–116
Böttcher G, Lilge S, Burgner-Kahrs J. Design of a reconfigurable parallel continuum robot with tendon-actuated kinematic chains. IEEE Robotics and Automation Letters, 2021, 6(2): 1272–1279
Yang C H, Geng S N, Walker I, Branson D T, Liu J G, Dai J S, Kang R J. 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
Chitalia Y, Jeong S, Yamamoto K K, Chern J J, Desai J P. Modeling and control of a 2-DoF meso-scale continuum robotic tool for pediatric neurosurgery. IEEE Transactions on Robotics, 2021, 37(2): 520–531
Park S, Kim J, Kim C, Cho K J, Noh G. Design optimization of asymmetric patterns for variable stiffness of continuum tubular robots. IEEE Transactions on Industrial Electronics, 2022, 69(8): 8190–8200
Oliver-Butler K, Childs J A, Daniel A, Rucker D C. Concentric push-pull robots: planar modeling and design. IEEE Transactions on Robotics, 2022, 38(2): 1186–1200
Girerd C, Morimoto T K. Design and control of a hand-held concentric tube robot for minimally invasive surgery. IEEE Transactions on Robotics, 2021, 37(4): 1022–1038
Rucker C, Childs J, Molaei P, Gilbert H B. Transverse anisotropy stabilizes concentric tube robots. IEEE Robotics and Automation Letters, 2022, 7(2): 2407–2414
Lee K, Wang Y Z, Zheng C Q. Twister hand: underactuated robotic gripper inspired by origami twisted tower. IEEE Transactions on Robotics, 2020, 36(2): 488–500
Santoso J, Onal C D. An origami continuum robot capable of precise motion through torsionally stiff body and smooth inverse kinematics. Soft Robotics, 2021, 8(4): 371–386
Wu S, Ze Q J, Dai J Z, Udipi N, Paulino G H, Zhao R K. 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
Kang B, Kojcev R, Sinibaldi E. The first interlaced continuum robot, devised to intrinsically follow the leader. PLoS One, 2016, 11(2): e0150278
Hawkes E W, Blumenschein L H, Greer J D, Okamura A M. A soft robot that navigates its environment through growth. Science Robotics, 2017, 2(8): eaan3028
Sadeghi A, Del Dottore E, Mondini A, Mazzolai B. Passive morphological adaptation for obstacle avoidance in a self-growing robot produced by additive manufacturing. Soft Robotics, 2020, 7(1): 85–94
Awtar S, Slocum A H. Constraint-based design of parallel kinematic XY flexure mechanisms. Journal of Mechanical Design, 2007, 129(8): 816–830
Howell L L, Midha A. A method for the design of compliant mechanisms with small-length flexural pivots. Journal of Mechanical Design, 1994, 116(1): 280–290
Ping Z Y, Zhang T C, Gong L, Zhang C, Zuo S Y. Miniature flexible instrument with fibre bragg grating-based triaxial force sensing for intraoperative gastric endomicroscopy. Annals of Biomedical Engineering, 2021, 49(9): 2323–2336
Wei X Y, Zhang Y X, Ju F, Guo H, Chen B, Wu H T. 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
Wang H D, Wang X L, Yang W L, Du Z J. Design and kinematic modeling of a notch continuum manipulator for laryngeal surgery. International Journal of Control, Automation, and Systems, 2020, 18(11): 2966–2973
Kato T, Okumura I, Kose H, Takagi K, Hata N. 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
Tian J W, Wang T M, Fang X, Shi Z Y. 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
Pei X, Yu J J, Zong G H, Bi S S. An effective pseudo-rigid-body method for beam-based compliant mechanisms. Precision Engineering, 2010, 34(3): 634–639
Acknowledgements
This work was supported in part by the National Natural Science Foundation of China (Grant No. U1813221) and the National Key R&D Program of China (Grant No. 2019YFB1311200).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, G., Yu, J., Tang, Y. et al. Design and modeling of continuum robot based on virtual-center of motion mechanism. Front. Mech. Eng. 18, 23 (2023). https://doi.org/10.1007/s11465-022-0739-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11465-022-0739-6