Compliant Constant-force Mechanism Research Articles

Topology Optimization of a Compliant Constant-Force End Effector for Robotic Operations Over Uneven Surfaces

Abstract A compliant constant-force mechanism (CCFM) is a specific type of compliant mechanism that serves as a passive force regulation device. When subjected to a load, it undergoes deformation, resulting in an almost consistent output force regardless of changes in input displacement. Traditional methods used to design CCFMs typically rely on either stiffness combination or parametric optimization based on existing design configurations. To enable the direct synthesis of CCFMs according to desired boundary conditions, this study proposes a systematic topology optimization method. This method includes a new morphology-based scheme designed to ensure the connectivity of the topological results, thereby achieving this objective. Using this approach, a CCFM suitable for end effector applications is designed and manufactured through 3D printing. Four of these CCFMs are then utilized to create an innovative compliant constant-force end effector for robotic operations on uneven surfaces. The experimental results demonstrate that the presented design achieves output force modulation through elastic deformation, eliminating the need for additional sensors and controllers to regulate the output force. The presented design can be mounted on a robotic arm to provide overload protection and maintain a consistent force output during operation when encountering irregular and uneven surfaces.

Buckling-induced instability in topology optimization of compliant constant-force mechanisms

Compliant constant-force mechanisms are compliant mechanisms that provide a nearly constant force over a prescribed deflection range. Topology optimization is an effective method for compliant constant-force mechanism design. However, instabilities caused by buckling often cause the optimization algorithm to fail to converge. This study analyzes the causes of buckling-induced instability and proposes methods to avoid this instability. A mechanism with three torsional springs is proposed, and its three force–displacement curves are analyzed. These bifurcated force–displacement curves cause the optimization algorithm to be unstable. Several topology optimization models with buckling constraints are proposed for designing compliant constant-force mechanisms. Their effects are tested and analyzed in numerical examples with different target constant forces and constant-force strokes. Almost all optimization results have three hinges, corresponding to a proposed mechanism with three torsion springs. A slight change in their initial design causes a large change in the force–displacement curve, which eventually leads to buckling-induced instability. This instability can be avoided by constraining the buckling load calculated at the configuration near the start of the constant-force stroke.

Safe Manipulation in Robotic Surgery Using Compliant Constant-Force Mechanism

Safe manipulation of soft tissue in robotic-assisted minimally invasive surgery (RMIS) is a challenging task for surgeons. The conventional solution is to introduce tactile sensors to measure the tool-tissue interaction force, and then transmit the signal back to the surgeon to enable manual force control. However, since the RMIS-forceps is very small, even the hand tremor of the surgeon could lead to unstable force applied to the tissue. To cope with this problem, we present a compliant constant-force mechanism (CFM) in this article to achieve stable force regulation of RMIS forceps. The proposed CFM is comprised of a pair of symmetrical compliant slider-crank mechanisms, whose mechanical behavior can be described by a pseudo-rigid-body (PRB) model. Cross-spring-based compliant joints are also introduced to improve the model accuracy, while the magnitude of the generated constant force can be adjusted by using detachable slider-crank mechanisms with different force configurations. In this work, the proposed CFM is selective-laser-sintered with polyamide (PA2200) and is actuated by a linear motor. Experiments were also conducted and successfully validated the constant-force performance of the proposed CFM. Furthermore, a grasping test of artificial artery was also performed, which demonstrated the application of the developed CFM system in RMIS.

Modular quasi-zero-stiffness isolator based on compliant constant-force mechanisms for low-frequency vibration isolation

To effectively isolate low-frequency vibrations, we present a rigid–flexible coupling quasi-zero-stiffness (QZS) vibration isolator with high-static-low-dynamic stiffness (HSLDS) characteristics. Specifically, the QZS isolator is realized by the development of a compliant constant-force mechanism, formed by parallelly combining a diamond-shape mechanism and a nonlinear bi-stable beam in parallel. To evaluate performance of the QZS isolator, we derived an analytical force–displacement model and dynamic model based on pseudo-rigid body method and Lagrange’s equations. Then, finite element analysis was performed in Workbench to verify theoretical analysis and identify the optimal design parameters. Furthermore, the dynamic responses of the QZS isolator are established with the harmonic balance method. Finally, the relationships among displacement transmissibility and factors including damping, BSB, payload mass, and material property are discussed. The results have shown that our QZS isolator design can effectively isolate vibrations in low frequency.

Construction process of a novel multi-degree of freedom parallel passive compliant constant-force mechanism

Based on the configuration of the Stewart parallel mechanism (SPM), after analyzing the kinetostatic characteristic of a planar four-bar linkage with attached springs which works around the kinematic limb-singularity, a process of constructing a novel multi-degree of freedom (DOF) parallel passive compliant constant-force mechanism (CCFM) is presented. The kinematic limb-singularity of a rigid four-bar linkage with attached springs is obtained and then is applied to construct a constant-force compliant mechanism (CM) based on the pseudo-rigid-body-model by designing appropriate structure parameters to obtain appropriate equivalent spring stiffness of flexures. The CCFM is further used as the branches of the SPM and then a passive multi-DOF parallel mechanism (PM) is constructed. Here the method of replacing the original rigid branch of the PM with the CCFM is called the “Expanded Rigid-body Replacement Synthesis” (ERBRS). The multi-DOF parallel passive CCFM can generate a constant-force zone when makes a small pose transformation around a certain position, where each compliant branch is located at the constant-force zone. The proposed CCFM can be applied in practice such as the polishing machine which needs the constant contact-force between the polishing head and the workpiece. The proposed method of constructing a CCFM with one- or multi-degree of freedom mechanism has some important reference value on designing other types of CCFMs.

Design of Passive Constant-Force End-Effector for Robotic Polishing of Optical Reflective Mirrors

Polishing plays an indispensable role in optical processing, especially for large-aperture optical reflective mirrors with freeform surfaces. Robotic polishing requires effective control of the contact force between the robot and the mirror during processing. In order to maintain a constant contact force during polishing, traditional polishing robots rely on closed-loop control of air cylinders, whose performances heavily rely on high-fidelity force sensing and real-time control. This paper proposes to employ a compliant constant-force mechanism in the end-effector of a polishing robot to passively maintain a constant force between the robot and the mirror, thus eliminating the requirement for force sensing and closed-loop control. The compliant constant force mechanism utilizing the second bending mode of fixed-guided compliant beams is adopted and elaborated for the passive end-effector. An end-effector providing a constant contact force of 40 N is designed and prototyped. The polishing experiment shows that the passive constant-force end-effector provides stable contact force between the robot and the mirror with fluctuation within 3.43 N, and achieves RMS (Root Mean Square) lower than λ/10 (λ = 632.8 nm) of the polished surface of the large-aperture optical reflective mirror. It is concluded that the constant-force compliant mechanism provides a low-cost and reliable solution for force control in robotic polishing.

FEA-based optimization and experimental verification of a typical flexure-based constant force module

To solve the problem of insufficient constant-force stroke of the compliant constant force mechanism (CFM), a FEA-based optimization method based on structural parameters is proposed in this paper. Firstly, a flexure-based constant force module (FBCFM) combined with a Z-shaped beam and a bi-stable beam is designed. By analyzing the force-displacement relationship of the two kind beams, the architectural parameters related to the constant force characteristic of the FBCFM are derived. Then, the initial constant-force stroke with 2.2 mm and output constant force with 13.8 N of the FBCFM are obtained by experimental studies. Furthermore, to explore the parametric effects for the designed FBCFM, parametric evaluation is conducted via MATLAB. Finally, the optimal solution set of architecture parameters is obtained with FEA-based optimization method. Through experimental verification, the constant-force stroke of the optimized FBCFM is 4.5 mm with constant force 8.5 N. The optimization results show the effectiveness and feasibility of the proposed FEA-based optimization method.

Topology Optimization for Design of a 3D-Printed Constant-Force Compliant Finger

A compliant constant-force mechanism is a passive force regulation device that can generate a nearly constant output force over a range of input or output displacements while without the use of sensors and feedback control. In topology synthesis of a compliant constant-force mechanism for a given input displacement range, the constant output force can be achieved by maintaining the output displacement to be nearly a same value while the input displacement increases. In order to further control the desired output displacement for the compliant constant-force mechanism before contacting the object, this article introduces a new composite objective function that can consider both the output force (with contact) and the output displacement (without contact) of the synthesized compliant mechanism. The sensitivity for the proposed objective function with respect to the element density is derived while considering the effect of nonlinearity in the large deformation condition. The proposed topology optimization method is used to design an innovative constant-force compliant finger, and its prototype is manufactured by 3-D printing using a flexible thermoplastic elastomer. The experimental results show the developed constant-force compliant finger can provide a nearly constant output force of 41.9 N over the input displacement ranging from 15 to 30 mm while the maximum and average force variations within the constant-force range are 2.2% and 0.9%, respectively. In addition, the developed constant-force compliant finger is used to design a three-fingered constant-force compliant gripper that can be used in robotic grasping of fragile objects.

Optimal Design of a Compliant Constant-Force Mechanism to Deliver a Nearly Constant Output Force Over a Range of Input Displacements

This study presents an optimal design procedure, including topology and geometry optimization methods to design a compliant constant-force mechanism, which can generate a nearly constant output force over a range of input displacements. The proposed constant-force mechanism is a passive force regulation device that can be used in various applications such as precision manipulation and overload protection. The numerical optimization problem is treated as an error minimization problem between output and objective forces. Both material and geometric nonlinearities are considered in topology and geometry optimization steps. Although the element stiffness for void and gray elements after topology optimization are quite small comparing with solid elements, their existence also contributes to the output force characteristic of the synthesized mechanisms. As these low-stiffness elements are not easy to manufacture in physical prototype, a helical compression spring is introduced in the topology optimized constant-force mechanism to account for the effect of low-stiffness elements, and an additional geometry optimization step is utilized to identify the spring constant as well as to fine-tune the geometric parameters. The optimized constant-force mechanism is prototyped by three-dimensional printing using flexible thermoplastic elastomer. The experimental results show that the proposed design can generate a nearly constant output force in the input displacement range of 3-6 mm. The developed constant-force mechanism is installed on an electric gripper drive mounted on a robot arm for robotic picking and placing application. Test results show the constant-force gripper can be used in handling of size-varied fragile objects.

Design and testing of a monolithic compliant constant force mechanism

This paper reports the design of a monolithic long-stroke constant force compliant mechanism (CM). The device is suitable for applications requiring a predefined force magnitude at the contact interface, such as manipulation systems. Starting from a compliant slider-crank mechanism providing a constant force within a rather limited deflection range, the paper describes the shape optimization carried out with the aim of extending the CM available stroke. In the first design step, the pseudo-rigid body (PRB) method is used to synthesize a sub-optimal lumped compliance solution. Secondly, two improved beam-based alternatives are evaluated by means of an integrated software framework, comprising Matlab and ANSYS. These new embodiments make use of a variable thickness beam, whose shape and dimensions have been optimized so as to provide a constant reaction force in an extended range. In particular, straight and spline segments are respectively used for the first and second prototype. With reference to the lumped compliance configuration, the available stroke has been increased of amounts equalling to 467% in the straight segments version (namely, from 3 mm to 14 mm) and to 833% in the spline segments version (namely, from 3 mm to 25 mm). All the predicted behaviors have been validated via physical experiments on 3D printed specimens. The proposed multi-step design flow may also be applied to a large variety of CMs, starting from their PRB model.

Optimization design of compliant constant-force mechanism for apple picking actuator

Low-destructive picking method is part of the key technologies for fruit-picking robots. To reduce the picking-induced fruit bruising during the clamping process, this paper realizes the constant output force required for low-destructive fruit clamping by setting the compliant mechanism on the end-effector and optimizing the mechanical characteristics of the compliant mechanism. Firstly, based on the shape function, the nonlinear ordinary differential equations of buckling deformation of compliant beams are established with boundary conditions. Secondly, the above boundary value problem is re-described as the initial value problem by using the shooting method, and the initial value optimization solution is combined with the genetic algorithm. Then, the sequence quadratic programming method is implemented to optimize the shape function of the beam to achieve constant force output within a certain deformation range. Taking apple picking as an example, the initial shape parameters of the compliant mechanism are set and the constant clamping force is obtained at about 7.9N. The above method is verified by the nonlinear finite element simulation, the force-displacement experiment and the apple clamping test. The compliant mechanism can provide the required grasping force and the successful grasping rate is about 95.3%. By properly adjusting the parameters of the compliant beam, the algorithm can also meet the requirements of constant force clamping for different types of fruit. The research provides a reference for the effective application of the compliant mechanism in low-destructive fruit-picking.

A Versatile 3R Pseudo-Rigid-Body Model for Initially Curved and Straight Compliant Beams of Uniform Cross Section

Rigid-body discretization of continuum elements was developed as a method for simplifying the kinematics of otherwise complex systems. Recent work on pseudo-rigid-body (PRB) models for compliant mechanisms has opened up the possibility of using similar concepts for synthesis and design, while incorporating various types of flexible elements within the same framework. In this paper, an idea for combining initially curved and straight beams within planar compliant mechanisms is developed to create a set of equations that can be used to analyze various designs and topologies. A PRB model with three revolute joints is derived to approximate the behavior of initially curved compliant beams, while treating straight beams as a special case (zero curvature). The optimized model parameter values are tabled for a range of arc angles. The general kinematic and static equations for a single-loop mechanism are shown, with an example to illustrate accuracy for shape and displacement . Finally, this framework is used for the design of a compliant constant force mechanism to illustrate its application, and comparisons with finite element analysis (FEA) are provided for validation.

Design and Control of a Novel Compliant Constant-Force Gripper Based on Buckled Fixed-Guided Beams

This paper presents the design and control of a novel gripper device with a passive type of compliant constant-force mechanism. The function of constant-force output is achieved by using the combination of a positive-stiffness and a negative-stiffness mechanism. The negative stiffness is generated by a bistable buckled fixed-guided beam. Conventionally, when gripping a target-object using a high-stiffness gripper, both the displacement control and force control are required to prevent the damage of the object. The uniqueness of the developed constant-force gripper is that it can eliminate the dependence on force control while keeping the force constant via its mechanical structure. The gripper performance is evaluated by the established analytical model and nonlinear finite-element analysis, and validated through experimental study on a fabricated prototype. To achieve a precise position output of the gripper jaw, a discrete-time variable structure control strategy based on a nonswitching type of reaching law is realized. The effectiveness of the gripper system is verified by conducting experimental studies on grasp-hold-release operations of a micro copper wire.

Compliant constant-force linear-motion mechanism

A fully compliant constant-force mechanism that uses an initially angled parallel-guiding mechanism is proposed. A pseudo-rigid-body model (PRBM) of the mechanism is developed and validated using both finite element models and experimental prototype testing. The PRBM is used as a preliminary design tool to identify parameters that result in a constant-force mechanism. An adjustable version of the mechanism is also proposed and is used to assess the range of validity of the PRBM and highlights how the system response can be varied by changing the flexible beams inclination. A finite element based optimization is used to create a modified version of the mechanism that incorporates beam-end rotation effects and offers greater performance. Potential applications for the mechanism are discussed and it is demonstrated as a component of a statically balanced system.

Dynamic analysis of compliant-based slider crank mechanism using the environments like ANSYS

A mathematical dynamic model is derived for the compliant-based slider crank chain mechanism. The compliant constant-force mechanism is a slider mechanism incorporating large-deflection beams, which outputs near-constant-force across the range of its designed deflection. The equation of motion is successfully validated with empirical data. The dynamic model is a cast for one of 28 possible configurations of compliant constant-force slider crank mechanism, identified by the type synthesis techniques. The author derived the dynamic model through Lagrange's equation for the selected configuration of compliant constant-force slider crank mechanism. An unexpected dynamic trait of the constant-force mechanism is discovered: There exists a range of frequencies for which the output force of the mechanism accords nearer to constant force than the output force at static levels.

Spatial compliant constant-force mechanism

In this study, a novel constant-force mechanism (CFM) is introduced. A design method is proposed to employ the compliant spatial slider-crank mechanism as CFM. Design geometry and initial conditions are presented for the selected configurations of the compliant constant-force mechanism (CCFM). Design parameters are nondimensionalized. Parameters of the PRBM that result in a CFM are determined via minimizing the variation in the output force over the given input displacement. A generalized solution method is derived to determine optimum results and some design charts are presented. In order to verify feasibility of the design procedure, a real model is built and it is shown that the experimental results are consistent with the theoretical approach.

A Numerical Method for Position Analysis of Compliant Mechanisms With More Degrees of Freedom Than Inputs

An underactuated or underconstrained compliant mechanism may have a determined equilibrium position because its energy storage elements cause a position of local minimum potential energy. The minimization of potential energy (MinPE) method is a numerical approach to finding the equilibrium position of compliant mechanisms with more degrees of freedom (DOF) than inputs. Given the pseudorigid-body model of a compliant mechanism, the MinPE method finds the equilibrium position by solving a constrained optimization problem: minimize the potential energy stored in the mechanism, subject to the mechanism’s vector loop equation(s) being equal to zero. The MinPE method agrees with the method of virtual work for position and force determination for underactuated 1-DOF and 2-DOF pseudorigid-body models. Experimental force-deflection data are presented for a fully compliant constant-force mechanism. Because the mechanism’s behavior is not adequately modeled using a 1-DOF pseudorigid-body model, a 13-DOF pseudorigid-body model is developed and solved using the MinPE method. The MinPE solution is shown to agree well with nonlinear finite element analysis and experimental force-displacement data.