Leveraging Geometry to Enable High-Strength Continuum Robots

Developing high-strength continuum robots can be challenging without compromising on the overall size of the robot, the complexity of design and the range of motion. In this work, we explore how the load capacity of continuum robots can drastically be improved through a combination of backbone design and convergent actuation path routing. We propose a rhombus-patterned backbone structure composed of thin walled-plates that can be easily fabricated via 3D printing and exhibits high shear and torsional stiffness while allowing bending. We then explore the effect of combined parallel and converging actuation path routing and its influence on continuum robot strength. Experimentally determined compliance matrices are generated for straight, translation and bending configurations for analysis and discussion. A robotic actuation platform is constructed to demonstrate the applicability of these design choices.

Compliance analysis and lightweight design of a two-degree-of-freedom rotating head

This article presents an approach for the compliance analysis and lightweight design of a two-degree-of-freedom rotating head by considering both gravity and joint/link compliances, which provides a comprehensive understanding on the posture adjustment mechanism of five-degree-of-freedom hybrid manipulator. A kinetostatic analysis is carried out to consider both externally applied wrench imposed upon the end-effector and gravity of all movable components. Then, a deflection analysis integrating both joint and link compliances and formulation of component compliance matrices are completed by using a semi-analytical approach. Finally, the lightweight design of two-degree-of-freedom rotating head is realized by considering the deflection constraints. This approach enables to effectively evaluate the deflections of end-effector caused by both payload and gravity under given operation conditions. Moreover, the established method provides reliable guidelines for the design of two-degree-of-freedom rotating head with superior static rigidities and dynamic behaviors.

A General Approach to the Large Deflection Problems of Spatial Flexible Rods Using Principal Axes Decomposition of Compliance Matrices

This paper presents a general discretization-based approach to the large deflection problems of spatial flexible links in compliant mechanisms. Based on the principal axes decomposition of structural compliance matrices, a particular type of elements, which relate to spatial six degrees-of-freedom (DOF) serial mechanisms with passive elastic joints, is developed to characterize the force-deflection behavior of the discretized small segments. Hence, the large deflection problems of spatial flexible rods can be transformed to the determination of static equilibrium configurations of their equivalent hyper-redundant mechanisms. The main advantage of the proposed method comes from the use of robot kinematics/statics, rather than structural mechanics. Thus, a closed-form solution to the system overall stiffness can be derived straightforwardly for efficient gradient-based searching algorithms. Two kinds of typical equilibrium problems are intensively discussed and the correctness has been verified by means of physical experiments. In addition, a 2DOF planar compliant parallel manipulator is provided as a case study to demonstrate the potential applications.

Synthesis of Point Planar Elastic Behaviors Using Three-Joint Serial Mechanisms of Specified Construction

This paper presents methods for the realization of 2 × 2 translational compliance matrices using serial mechanisms having three joints, each either revolute or prismatic and each with selectable compliance. The geometry of the mechanism and the location of the compliance frame relative to the mechanism base are each arbitrary but specified. Necessary and sufficient conditions for the realization of a given compliance with a given mechanism are obtained. We show that, for an appropriately constructed serial mechanism having at least one revolute joint, any single 2 × 2 compliance matrix can be realized by properly choosing the joint compliances and the mechanism configuration. For each type of three-joint combination, requirements on the redundant mechanism geometry are identified for the realization of every point planar elastic behavior at a given location, just by changing the mechanism configuration and the joint compliances.

Standardized Compliance Matrices for General Anisotropic Materials and a Simple Measure of Anisotropy Degree Based on Shear-Extension Coupling Coefficient

The compliance matrix for a general anisotropic material is usually expressed in an arbitrarily chosen coordinate system, which brings some confusion or inconvenience in identifying independent elastic material constants and comparing elastic properties between different materials. In this paper, a unique stiffest orientation-based standardized compliance matrix is established, and 18 independent elastic material constants are clearly shown. During the searching process for the stiffest orientation, it is interesting to find from our theoretical analysis and an example that a material with isotropic tensile stiffness does not definitely possess isotropic elasticity. Therefore, the ratio between the maximum and minimum tensile stiffnesses, although widely used, is not a correct measure of anisotropy degree. Alternatively, a simple and correct measure of anisotropy degree based on the maximum shear-extension coupling coefficient in all orientations is proposed. However, for a two-dimensional constitutive relation, both the stiffness ratio and the shear-extension coupling coefficient can be adopted as proper measures of anisotropy degree.

Towards Computer Aided Design and Analysis of Spatial Flexure Mechanisms

Flexure mechanisms are the central part of numerous precision instruments and devices that are used in a wide range of science and engineering applications and currently, design of flexure mechanisms often heavily relies on designers’ previous hands-on experience. Therefore, a design tool that will speed up the design process is needed and this paper will introduce a systematic approach for building the necessary equations that are based on screw theory and linear elastic theory to analyze flexure mechanisms. A digital library of commonly used flexure elements must be available for a design tool and therefore, we first present the compliance matrices of commonly used flexure components. Motion twists and force wrenches of the screw theory can be related with these compliance matrices. Then, we introduce an algorithm that constructs the required linear system equations from individual compliance equations. This algorithm is applicable to flexure mechanisms with serial, parallel or hybrid chains. Finally, the algorithm is tested with a flexure mechanisms and it is shown that this approach can be the core of a future design tool.

Force Analysis of Spatial Single Closed-Loop Overconstrained Mechanisms

Taking the Bennett and Schatz mechanisms as examples, force analyses of spatial single closed-loop (SSCL) overconstrained mechanisms are demonstrated aiming to obtain the driving forces/torques and joint reactions of this kind of mechanisms. Firstly, regarding the SSCL overconstrained mechanisms as parallel mechanisms with two supporting limbs, the constraint wrenches and actuation wrenches imposed on the moving platform by the two limbs are discussed, and the mobility of each mechanism is analyzed based on the screw theory. Then, the compliance matrices of the limbs’ constraint wrenches are derived, which contribute to solve the statically indeterminate force problem of the mechanisms. Next, by combining the force and moment equilibrium equation of the moving platform with the deformation compatibility equation of the corresponding mechanism, the magnitudes of all constraint wrenches and actuation wrenches are solved. Furthermore, the driving forces/torques and joint reactions are derived. Finally, the numerical and simulation results of the two mechanisms are presented.

Program Tools for Residual Stress Evaluation by Ring-Core Method

Residual stress determination requirements of production and research users grow rapidly. Commercially available programs enable relatively quick residual stress evaluation with certain level of accuracy and with limited user access to used compliance matrices and calculations. However precise analyses require sensitive approach to compliance matrices determined for individual case e.g. for specific specimen dimensions. Therefore program tools for complex residual stress evaluation by Ring-Core method were developed using finite element analysis and Visual Basic scripts.

A Compliance-Based Parameterization Approach for Type Synthesis of Flexure Mechanisms

This paper presents an approach based on parameterized compliance for type synthesis of flexure mechanisms with serial, parallel, or hybrid topologies. The parameterized compliance matrices have been derived for commonly used flexure elements, which are significantly influenced by flexure parameters including material and geometric properties. Different parameters of flexure elements generate different degree of freedom (DOF) characteristic of types. Enlightened by the compliance analysis of flexure elements, a parameterization approach with detailed processes and steps is introduced in this paper to help analyze and synthesize flexure mechanisms with the case study as serial chains, parallel chains, and combination hybrid chains. For a hybrid flexure, the results of finite element (FE) modeling simulations are compared to analytical compliance elements characteristic. Under linear deformations, the maximum compliance errors of analytical models are less than 6% compared with the FE models. The final goal of this work is to provide a parameterized approach for type synthesis of flexure mechanisms, which is used to configure and change the parameters of flexure mechanisms to achieve the desired DOF requirements of types initially.

In-Plane Compliances of Planar Flexure Hinges With Serially Connected Straight- and Circular-Axis Segments

The paper introduces a new category of planar flexure hinges that are formed by serially connecting variable cross-sectional segments of straight longitudinal axes with segments of circular longitudinal axes. The small-displacement compliance analytical model is derived for a general hinge configuration using a matrix approach that sums the transformed local-frame compliance matrices of individual component segments. The particular class of antisymmetric flexure hinges is studied using the general model and the corresponding global-frame compliance matrix is calculated as a linear combination of compliances defining the half-hinge configuration. A serpentine (folded) flexure hinge is introduced to illustrate the generic antisymmetric design and model. Finite element simulation is used to validate the analytic compliances of this particular configuration and the compliance sensitivity to geometric parameters variation is further analyzed. The translation stiffnesses of a planar-motion stage with two identical serpentine hinges are calculated based on hinge compliances. The optimum hinge design is subsequently identified, which realizes minimum-resistance motion along the stage axial motion direction.