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Continuum manipulators coupled with magnetic actuation have great potential as steerable instruments for diverse surgical applications. They can be maneuvered inside the human body to reach difficult-to-access surgical sites with contactless actuation. This paper presents a new design of a compliant continuum manipulator of diameter 3 mm and length 70 mm, capable of spatial bending under magnetic actuation. A quasi-static model is developed to estimate the 3D motion of the manipulator. Experiments report an overall mean error in whole shape estimation of the manipulator between the model and the ground truth of 1.7 mm and 4.8 mm, when suspended vertically and horizontally from its base, respectively. Furthermore, fiber Bragg grating (FBG) sensors are integrated with the manipulator to enable shape sensing. Closed-loop control is demonstrated to trace different trajectories with the tip of the manipulator. A square trajectory and a straight line trajectory are generated with an average error in tip position of 4.1 mm between the desired and estimated positions. The potential of the manipulator as a steerable instrument is validated by maneuvering it inside phantoms of a bifurcating arterial system and a heart with visual guidance from a miniature camera.

Magnetic continuum manipulators (MCMs) are a class of continuum robots that can be actuated without direct contact by an external magnetic field. MCMs operating in confined workspaces, such as those targeting medical applications, require flexible magnetic structures that contain combinations of magnetic components and polymers to navigate long and tortuous paths. In cylindrical MCM designs, a significant trade-off exists between magnetic moment and bending flexibility as the ratio between length and diameter decreases. In this study, we propose a new MCM design framework that enables increasing diameter without compromising on flexibility and magnetic moment. Magnetic soft composite helices constitute bending regions of the MCM and are separated by permanent ring magnets. Local dipole interactions between the permanent magnets can reduce bending stiffness, depending on their size and spacing. For the particular segment geometry presented herein, the local dipole interactions result in a 31 % increase in angular deflection of composite helices inside an external magnetic field, compared to helices without local interactions. Also, we demonstrate fabrication, maneuverability, and example applications of a multi-segment MCM in a phantom of the abdominal aorta, such as passing contrast dye and guidewires.

Magnetic actuation is a versatile technology, widely applied in medical robotics for noncontact steering of flexible instruments and untethered agents. In this article, we exploit the benefits of this technology by developing a magnetically actuated flexible catheter capable of the controlled ejection and retrieval of an untethered magnetic capsule. The catheter is actuated by the advanced robotics for magnetic manipulation system. The scanning ultrasound is used for 3-D shape reconstruction of the catheter, with a mean error of 0.37 mm. We use a closed-loop position controller to steer the catheter, reporting a mean error of 0.82 mm. We develop a dynamic model of the capsule and use it to predict the trajectory of the projectile. We demonstrate the targeting of the capsule utilizing the null-space of the catheter actuation (mean residual tip displacement of 0.8 mm). Finally, we perform a delivery of a capsule to and retrieval from a target inaccessible for the catheter tip, demonstrating the capability of our instrument to reach challenging locations.

Accurate estimation of deformed shape and reaction forces poses a significant challenge in modeling and control of continuum manipulators interacting with their environment. This paper presents a framework for the analysis of a continuum manipulator subjected to multiple external loads using pseudo rigid body (PRB) modelling method. A PRB model with six degrees of freedom is developed, and the statics equations for a manipulator with multiple loads are presented, followed by the approach for determining the optimal model parameters. Dimensionless constants are used to enable scaling the model to manipulators of different lengths and materials. The approach is first validated by a comparison with Finite Element Analysis, and the results show a low error in estimating the tip deflection (less than 1% of the manipulator length). A magnetically-actuated manipulator driven by an array of electromagnetic coils is used for experimental validation. The optimization for a single segment of the manipulator is performed with experimental data, with an average error of 2.2 mm in calculating the tip position. An experimental setup for a manipulator with multiple loads is created by introducing displacement constraints with fixtures connected to multi-axis force sensors. The model shows good agreement with quasi-static experiments in estimating the reaction forces and predicting the deformed shape of the manipulator. The average error in force estimation is 61 mN, while the average error in estimating tip position is 2.8 mm for a manipulator length of 82 mm. (C) 2019 Elsevier Ltd. All rights reserved.

Magnetically-guided catheters present a promising treatment option to reduce the incidence of post-operative trauma in minimally invasive procedures. In this study, we present a novel catheter design that combines the characteristics of standard angiography and angioplasty catheters in combination with magnetic guidance. The catheter body consists of a 5F size angiography catheter that has been adapted to hold an intra-aortic balloon (8F diameter). It uses two magnets, one for tip guidance and another for easy steering into blood vessel branches. Magnetic guidance of the catheter is demonstrated using an array of six mobile electromagnetic coils with a custom-built graphical user interface. A 3R pseudo-rigid-body model is used within a closed-loop controller to calculate the coil currents and positions to obtain the required magnetic field in order to control the orientation of the catheter tip. Magnetic guidance of the catheter is demonstrated in a phantom model of the aorta. The angiography and angioplasty capabilities of the catheter are illustrated through separate experiments.

In the past decade, remote actuation through magnetic fields has been used for position and orientation control of continuum manipulators (CMs) with a single magnet at the distal tip. By leveraging multiple points of actuation along the length of the CM it is possible to achieve increasingly complex shapes, which could be of interest in complex navigation tasks, for example, in minimally invasive surgery. In this study we present an approach for multi-point orientation control of discretely magnetized CMs. The approach is demonstrated with a manipulator that contains two permanent magnets, which are each actuated inside a non-homogeneous magnetic field. We formulate an accurate field model that conforms to Maxwell's equations and apply this to the available actuation system. Furthermore, Cosserat rod theory is used to model the manipulator deformation under external wrenches, and is utilized to numerically compute a Jacobian necessary to calculate the actuation inputs. During experiments, a stereo vision setup is used for manipulator shape feedback. Target orientations are manually provided as input to show independent orientation control of the two permanent magnets. Additionally, simulations with an extended virtual clone of the electromagnetic system are performed to show the capability of achieving more complex manipulator shapes. In both scenarios, it is observed that the algorithm is able to independently control the orientation of two interconnected magnets in a non-uniform magnetic field.

Current surgical devices are mostly rigid and are made of stiff materials, even though their predominant use is on soft and wet tissues. With the emergence of compliant mechanisms (CMs), surgical tools can be designed to be flexible and made using soft materials. CMs offer many advantages such as monolithic fabrication, high precision, no wear, no friction, and no need for lubrication. It is therefore beneficial to consolidate the developments in this field and point to challenges ahead. With this objective, in this article, we review the application of CMs to surgical interventions. The scope of the review covers five aspects that are important in the development of surgical devices: (i) conceptual design and synthesis, (ii) analysis, (iii) materials, (iv) manufacturing, and (v) actuation. Furthermore, the surgical applications of CMs are assessed by classification into five major groups, namely, (i) grasping and cutting, (ii) reachability and steerability, (iii) transmission, (iv) sensing, and (v) implants and deployable devices. The scope and prospects of surgical devices using CMs are also discussed.

Continuum robots have the potential to form an effective interface between the patient and surgeon in minimally invasive procedures. Magnetic actuation has the potential for accurate catheter steering, reducing tissue trauma and decreasing radiation exposure. In this paper, a new design of a monolithic metallic compliant continuum manipulator is presented, with flexures for precise motion. Contactless actuation is achieved using time-varying magnetic fields generated by an array of electromagnetic coils. The motion of the manipulator under magnetic actuation for planar deflection is studied. The mean errors of the theoretical model compared to experiments over three designs are found to be 1.9 mm and 5.1 deg in estimating the in-plane position and orientation of the tip of the manipulator, respectively, and 1.2 mm for the whole shape of the manipulator. Maneuverability of the manipulator is demonstrated by steering it along a path of known curvature and also through a gelatin phantom, which is visualized in real time using ultrasound imaging, substantiating its application as a steerable surgical manipulator.

Soft materials with embedded magnetic properties can be actuated in a contactless manner for dexterous motion in restricted and unstructured environments. Magnetic soft robots have been demonstrated to be capable of versatile and programmable untethered motion. However, magnetic soft robots reported in literature are typically actuated by utilizing magnetic fields to generate torques that produce deformation. By contrast, this work investigates the utilization of field gradients to produce tethering forces for anchoring soft robots to the working surface, in conjunction with the use of magnetic fields to generate torques for deformation. The methodology applied here uses a six-coil electromagnetic system for field generation. The approach to achieve the magnetic field and gradients desired for soft robot motion is described, along with the restrictions imposed by Maxwell’s equations. The design and fabrication of the soft robots is explained together with calculations to assess the capabilities of the actuation system. Proof-of-concept demonstrations of soft robot motion show Hexapede robots with the ability to ‘walk’ untethered on the ceiling of the workspace, working against gravity; and lightweight Worm robots made of thin strips of material are demonstrated to locomote while staying in contact with the ground.

Flexure mechanisms are the central part of precision instruments and devices for numerous science and engineering applications. Currently, design of flexure mechanisms often heavily relies on finite element analysis. However, the modeling complexity and low computational efficiency make it not suitable for the early design stage when many concepts need to be evaluated in a short period of time. To reduce the overhead in the conceptual design stage, we present a multi-segment energy minimization framework that integrates linear elastic theory for kinetostatic analysis of spatial flexure mechanisms. Compliance matrices for commonly used flexure elements are presented and their accuracy was studied and verified in detail. While deformation of each individual segment depends on the linear elastic theory, the multi-segment model allows accurate calculation of large deformations with high computational efficiency. To facilitate modeling of spatial flexure mechanisms, we have also implemented rich Graphical User Interfaces (GUI) in MATLAB environment. The proposed framework and software tool are tested with spatial mechanisms in which nonlinear kinematic constraints and combined loading are present. The examples showed that the proposed multi-segment framework can accurately capture large kinematic motion subjected to complex loading.

Circular beams can offer potential advantages to designers of compliant mechanisms and provide useful alternatives to other types of compliant elements. However, they pose unique challenges due to lack of effective models for predicting deformation upon loading. In this work, the kinematic and stiffness properties of circular beams with uniform cross sections subjected to combined force and moment loads are represented using pseudo-rigid-body models. The pseudo-rigid-body models serve as numerical approximations for easy derivation of mechanism equations, and also enable quick solutions using multi-body software packages. The models are derived by comparisons against beam theory, and the values of the parameters are presented in the form of fitting functions for a large range of arc angles. The validity and applicability of these models in analysis are demonstrated with the example of a micro-force sensor. Their use in design is demonstrated with the case of developing flexure mechanisms for microspines in grasping applications, with comparisons against Finite Element Analysis to prove their accuracy and speed. The PRB models can serve as tools facilitating design of compliant mechanisms with circular beams.

This paper details the mechanical design and control of a human safety robotic arm with variable stiffness, starting from conceptual design to prototype. The mechanism designed is based on parallel guided beam with a roller slider actuated by a power screw and a DC motor with an encoder for position feedback. Unlike conventional robotic systems that control the stiffness in joints, this design introduces compliance to the robotic arm link itself. By controlling the slider position, the effective length of the link can be adjusted to provide the necessary stiffness change. A PID position controller is employed and the position accuracy is experimentally evaluated. The stiffness variation of the prototype is validated by experiments and FEA simulation. The overall stiffness change achieved is 20-fold.

This paper focuses on developing a framework for determining the optimal pseudo-rigid-body (PRB) model of 2D cantilever beams. PRB models are commonly used in design and analysis of compliant mechanisms since they significantly reduce the number of degrees of freedom compared with the finite element approach. Although a number of PRB models are available in literature, there is not a unified method to determine the most suitable pseudo-rigid-body model for a specific application. In this work, we first study a modified Timoshenko beam equation which accommodates shear forces and axial deformation. The numerical solution to the Timoshenko beam equation provides a baseline for comparing various models. A novel concept of “PRB matrix” is proposed for representing topologies of all PRB models in a uniform way. The optimal set of kinematic parameters (characteristic lengths and spring constants) of PRB models are determined by minimizing the error of tip deflection and comparing with the solution of the Timoshenko beam equation. To validate this formulation, we compare the results with existing PRB models and obtained equivalent if not a more accurate set of PRB parameters. At last, a case study of a compliant slider mechanism is provided to demonstrate the accuracy of two PRB models in this particular application.

The use of pseudo-rigid-body models in the analysis and design of compliant mechanisms has opened up the possibility of using various types of flexible elements within the same framework. In this paper, an idea for combining initially curved and straight beams within compliant mechanisms is developed to create a set of equations that can be easily used to analyze various designs and topologies. A pseudo-rigid-body model with three revolute joints is derived to approximate the behavior of initially-curved compliant beams, to go with another model previously presented for straight beams. The general kinematic and static equations for a single-loop mechanism are shown. Finally, this setup is used for the early-stage design of a compliant constant force mechanism to illustrate its application and comparisons with Finite Element Analysis for validation.

This paper seeks to speed up the topology optimization using a pseudorigid-body (PRB) model, which allows the kinetostatic equations to be explicitly represented in the form of nonlinear algebraic equations. PRB models can not only accommodate large deformations but more importantly reduce the number of variables compared to beam theory or finite element methods. A symmetric 3R model is developed and used to represent the beams in a compliant mechanism. The design space is divided into rectangular segments, while kinematic and static equations are derived using kinematic loops. The use of the gradient and hessian of the system equations leads to a faster solution process. Integer variables are used for developing the adjacency matrix, which is optimized by a genetic algorithm. Dynamic penalty functions describe the general and case-specific constraints. The effectiveness of the approach is demonstrated with the examples of a displacement inverter and a crimping mechanism. The approach outlined here is also capable of estimating the stress in the mechanism which was validated by comparing against finite element analysis. Future implementations of this method will incorporate other pseudorigid-body models for various types of compliant elements and also try to develop multimaterial designs.

The initial design of compliant mechanisms for a specific application can be a challenging task. This paper introduces a topology optimization approach for planar mechanisms based on graph theory. It utilizes pseudo-rigid-body models, which allow the kinetostatic equations to be represented as nonlinear algebraic equations. This reduces the complexity of the system compared to beam theory or finite element methods, and has the ability to incorporate large deformations. Integer variables are used for developing the adjacency matrix, which is optimized by a genetic algorithm. Dynamic penalty functions describe the general and case-specific constraints. A symmetric 3R model is used to represent the beams in the mechanism. The design space is divided into rectangular segments while kinematic and static equations are derived using kinematic loops. The effectiveness of the approach is demonstrated with the example of an inverter mechanism. The results are compared against finite element methods to prove the validity of the new model as well as the accuracy of the approach outlined here. Future implementations of this method will include stress and deformation analysis and also introduce multi-material designs using different pseudo-rigid-body models.

Compliant members come in a variety of shapes and sizes. While thin beam flexures are commonly used in this field, they can be replaced by soft members with lower aspect ratio. This paper looks to study the behavior of such elements by analyzing them from the view of beam theory for 2D cases. A modified version of the Timoshenko beam theory is presented which incorporates extension and Poisson's effects. The utility and validity of the new approach are demonstrated by comparing against Euler–Bernoulli beam theory, Timoshenko beam theory, and finite-element analysis (FEA). The results from this are then used to study the performance of pseudo-rigid-body models (PRBMs) for the analysis of low aspect ratio soft compliant joints for 2D quasi-static applications. A parallel-guiding mechanism comprised of similar compliant elements is analyzed using the new results to validate the contribution of this work.

Compliant mechanisms achieve motion utilizing deformation of elastic members. However, analysis of compliant mechanisms for large deflections remains a significant challenge. In this paper, a three-spring revolute–prismatic–revolute (RPR) pseudorigid-body (PRB) model for short beams used in soft joints made of elastomer material is presented. These soft joints differ from flexure-based compliant joints in which they demonstrate significant axial elongation effects upon tip loadings. The traditional PRB models based on long thin Euler beams failed to capture this elongation effect. To overcome this difficulty, a model approximation based on the Timoshenko beam theory has been derived. These equations are utilized to calculate the tip deflection for a large range of loading conditions. An optimization process is then carried out to determine the optimal values of the parameters of the PRB model for a large range of tip loads. An example based on a robotic grasper finger is provided to demonstrate how the model can be used in analysis of such a system. This model will provide a simple approach for the analysis of compliant robotic mechanisms.

Pseudo-rigid-body models serve as a convenient numeric tool for the analysis of compliant elements. However, most PRB models are derived on the basis of Euler beam equations, without accounting for the effect of deformation on beam geometry. In this paper, we look at the effects of deformation on length and cross section of the beam, and try to understand these phenomena with respect to some dimensionless parameters. These effects are more pronounced for short beams of soft materials. A few PRB models listed in literature are compared against FEA results, and optimization methods are used to determine more accurate PRB models for varying beam geometry. A study of these results will guide the discussion on how the accuracy of the PRB models changes with the beam parameters. An example of a compliant mechanism which experiences significant axial loads will be used to prove the validity of these results.Copyright © 2015 by ASME

Compliant mechanisms achieve motion utilizing deformation of elastic members. However, analysis of compliant mechanisms for large deflections remains a significant challenge. In this paper, we will develop a 3-spring pseudo-rigid-body model for 2D beams that are often used in compliant joints in robots. First, we utilize the Timoshenko beam theory to calculate the tip deflection for a large range of loading conditions. An optimization process is then carried out to calculate the values of the parameters of the PRB model. The errors in the model will be analyzed and compared to the beam model. An example based on a robotic grasper finger is provided to demonstrate how the model can be used in analysis of such a system. This model will provide a much simpler approach for the analysis of compliant robotic mechanisms.Copyright © 2014 by ASME