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• Revised chained beam constraint model extended for variable section beams. • Developed kinetostatic model for FRE finger with trapezoidal beams. • Systematically analyzed how the width and thickness variations affect grasping. • Trapezoidal finger design outperforms uniform in grasp tests. Adaptive grasping of diverse objects is crucial for soft robotic fingers. The design of trapezoidal variable-section beams is increasingly recognized for its potential to enhance grasping performance of soft fingers. Despite this widespread interest, a significant gap exists in systematic research investigating how the corresponding structural design enables profound performance effects. The primary challenge hindering such progress pertains to the intricate kinetostatic modeling of fingers, particularly considering variable-section beams. This paper presents a comprehensive closed-form kinetostatic model for a biomimetic fin ray effect (FRE) soft robotic finger based on the modified chained-beam-constraint model. Utilizing a geometry-based contact constraint technique that satisfies the minimum strain energy principle, our model facilitates analysis of stiffness variations and the overall energy dynamics of the finger. We systematically explore the impact of width and thickness variations along the length of longitudinal beams on crucial aspects of grasping performance, including stiffness, energy consumption and adaptability. Our results, which were validated through finite element analysis (FEA) and experiments, demonstrate a tangible improvement in grasp performance over uniform design. [ABSTRACT FROM AUTHOR]

Highlights • A generalized analytical compliance modeling method regarding flexure hinges is proposed. • A compliance relationship between base segment and its mirrored segment is established. • Closed-form compliances and precision equations of hybrid flexure hinges are derived. • Compliances of six left-half conic-section flexure segments are formulated. Abstract This paper presents a generalized analytical compliance model that can quickly formulate the equations of compliance and precision for hybrid flexure hinges. Inspired by the combined design of multiple flexure segments connected serially, a large number of hybrid flexure hinges are designed, which can be equivalent to serial flexible chains comprised of multiple pre-defined flexure segments. Compliance matrix for each flexure segment can be obtained only through a few designated base segments of known compliances. By drawing from the compliance modeling process of serial flexible chains, the capacity and precision of rotation of hybrid flexure hinges are easily evaluated in terms of geometric parameters and compliances of base segments, as well as numerous and tedious integral operations are effectively avoided. Additionally, a representative set of flexure configurations with conic-section flexure segments and the finite element simulations are introduced to validate the analytical model. Finally, several numerical simulations in regard to the motion accuracy of flexure hinges are carried out to study the effects of geometric parameters. [ABSTRACT FROM AUTHOR]

Abstract Based on the modified Grübler–Kutzbach (G–K) criterion and relative degrees of freedom (RDOF) criterion, a novel method is proposed for structural synthesis of a class of kinematically redundant parallel manipulators (KR-PMs) with spherical joints attached to a moving platform. First, a formula that can be used to calculate the number of kinematic joints not limited to basic joints is proposed, which is affected by the number of links including fixed base, links with multi-node, compound hinges, and the INTERNAL independent loops in parallel manipulators. Furthermore, the sum degrees of all the kinematic joints possesses a direct relationship with the number of kinematic joints, the number of spherical joints, and the type combination of spherical joints attached to the moving platform. Then, the relationship between the mobility M and the RDOF with intermediate variables is derived based on modified G-K criterion and RDOF criterion, which is the base of the proposed synthesis procedure. Next, the proposed synthesis procedure is performed with the synthesis conditions RDOF = 3 or 4, and some typical KR-PMs are obtained. Finally, the condition for proper selection of actuators for KR-PM is revealed. And the reasons for large configuration randomness of the synthesized KR-PMs are discussed. [ABSTRACT FROM AUTHOR]

Reconfigurable parallel mechanisms (RPMs) have the advantages of high stiffness, good dynamic performance due to their parallel structures, and can reconfigure themselves into various mobility configurations to accommodate different task requirements, which indicate that RPMs have the potential to be used in multidirectional additive manufacturing. Based on this application, this paper focuses on the design and analysis of a novel RPM. Degree of freedom (DOF) requirements in different stages of multidirectional additive manufacturing are analyzed. A hybrid limb that is composed of a planar metamorphic mechanism and a 4-DOF serial chain is presented, and then employed in the design of a three-legged RPM. Unified model for kinematic position analysis and the overall Jacobian matrix of the RPM are established. Singularity analysis including inverse kinematic singularity and direct kinematic singularity analysis are conducted. Workspaces of the RPM in different operation modes are evaluated. A prototype and some experiments are presented. [ABSTRACT FROM AUTHOR]

• A novel 3- P RS-finger-based parallel dexterous hand (PDH) is proposed. • The PDH can perform 6-DOF in-hand manipulation with bidirectional pinching. • The PDH have the possibility to achieve a good force transmission capability. • The PDH can complete the accurate control of in-hand manipulation. Considering the defects of the traditional dexterous hand in precise in-hand manipulation and bidirectional pinching capability, this paper proposes a 3- P RS-finger-based parallel dexterous hand (PDH). The PDH structure is composed of three 3- P RS parallel fingers. First, a pinching shape analysis is conducted to demonstrate the PDH's bidirectional pinching capability. Then, by analyzing the workspace of the PDH pinching nine objects, the influence on the in-hand manipulation workspace of different objects is determined. The PDH can perform symmetrical in-hand manipulation to address the issue that almost all humanoid dexterous hands pinch objects in a single direction. The force transmission capability of the PDH is compared with that of the 3R serial dexterous hand (SDH) under the same trajectory. The results indicate that the PDH have the possibility to possess a good pinching force performance through the specific trajectory planning. Bidirectional pinching experiments are conducted, and the experimental results demonstrate that the PDH can realize the accurate in-hand manipulation under almost frictionless conditions. The proposed PDH provides a feasible design for the theoretical development and practical application of dexterous hands. [ABSTRACT FROM AUTHOR]

• An approach for constructing the 3-DOF single-loop parallel leg mechanism is proposed. • Equivalent drive mechanisms are presented to substitute the serial chains with two serial actuated joints. • A novel class of 3-DOF single-loop parallel leg mechanisms with 3T/1R2T/2R1T motions are constructed. • The performances are analyzed to show that the novel leg mechanisms possess more advantages. • The simulation is provided to illustrate the omnidirectional walk of quadruped robot. This paper presents a class of novel 3-degree-of-freedom (DOF) single-loop parallel leg mechanisms for walking robots. An approach for constructing the 3-DOF single-loop parallel leg mechanism is proposed. The single-loop parallel leg mechanism is composed of a serial limb with two actuated joints and a serial limb with one actuated joint, where two serial actuated joints of a limb are replaced by an equivalent drive mechanism. The novel legs can generate three translation (3 T), two rotation and one translation (2 R 1 T), and one rotation and two translation (1 R 2 T) motions, which make the workspace of the foot-endpoint three-dimensional in volume, and the robots can walk flexibly and omnidirectionally. Compared with existing leg mechanisms, the novel leg mechanisms have the potential advantages of larger step length and step height. This will enable the walking robot to move faster and step over larger obstacles. A quadruped robot is built with novel leg mechanisms, and its performances are analyzed and omnidirectional walk is demonstrated by simulation. [ABSTRACT FROM AUTHOR]

With the deepening and refinement of research, the traditional parallel mechanisms (PMs) have become increasingly hard to satisfy the demands of high rotational performance, decoupled motions, or some other specific motion properties. This paper focuses on the synthesis of a class of generalized parallel mechanisms (GPMs), which are capable of preserving the advantages and overcoming the shortcomings of the traditional PMs. Inspired by the closed-loop mechanisms with one or two dimensional high output performance and based on the characteristics of the set mapping and the group operations, a novel method about the synthesis of GPMs is proposed. By means of this method, a type of four degree of freedom (4-DOF) GPMs which contain 2T2R (T denotes a translational DOF and R represents a rotational DOF), 3T1R, and 1T3R categories are synthesized and further a kind of 5-DOF GPMs which are divided into 3T2R and 2T3R categories are obtained. The synthesis method is universal for the design of the GPMs and the proposed GPMs possess high performance because the articulated platforms are evolved from the well-known planar closed-loop linkage mechanisms. [ABSTRACT FROM AUTHOR]

This article focuses on the synthesis and analysis of a class of novel 2T2R (T denotes Translation and R denotes Rotation) and 3T2R parallel mechanisms (PMs) with large decoupled output rotational angles. Two articulated moving platforms (AMPs) composed by revolute joints are proposed. A common parallelogram and an evolution parallelogram which are used to orient the rotation axes of the AMPs are designed and analyzed. By means of Lie group theory, the limbs connected in the AMPs are enumerated and two types of 2T2R PMs are synthesized. Then, based on the proposed 2T2R PMs, a family of 3T2R PMs are obtained through adding a translational degree of freedom (DOF). The fact that the orthogonal arrangement of the revolute joints in the AMPs eliminates the interference between the two rotations guarantees the high rotational performance of the manipulators. Finally, the inverse kinematics of the example PM is conducted and the workspace is obtained to illustrate the high rotational capability. [ABSTRACT FROM AUTHOR]

Abstract: This paper focuses on a diamond kinematotropic chain which is integrated in the construction of a new family of reconfigurable parallel mechanisms. The branch transition of the planar diamond kinematotropic chain is analyzed and the equivalent kinematic joints corresponding to each motion branch are identified. Kinematic limbs that can provide a constraint force and a constraint couple are enumerated based on screw theory. Sixteen reconfigurable limbs which are capable of decoupling the constraint force and the constraint couple in the reconfigured configurations are constructed by integrating the diamond kinematotropic chain. A family of reconfigurable parallel mechanisms having three identical kinematic limbs is structured by connecting the platform to the base with reconfigurable limbs. The platform of each reconfigurable parallel mechanism has ability to perform variable motion modes such as 3T, 2T1R, 2R1T and 3R. One of the reconfigurable parallel mechanisms is sketched as example and the actuation scheme for the mechanisms in this family is discussed. [Copyright &y& Elsevier]