Single-loop Mechanisms Research Articles

Structural–parametric synthesis of single-loop 6R and 7R mechanisms using factorization of motion polynomials and its application in grippers

Abstract In this study, the so-called quasi-spiral motion pattern of a particular 3R (revolute) chain, which could track a quasi-spiral curve, is discovered for application in envelope gripping. Naturally, a novel perspective on the synthesis of 1-DOF (degree of freedom) single-loop 6R and 7R mechanisms is presented to implement the quasi-spiral motion pattern. In these processes, the method of factorization of the motion polynomial is used to synthesize a series of single-loop mechanisms with the motion to generate quasi-spiral curves. By employing the proposed method, numerous innovative 6R and 7R mechanisms have been developed to construct dual layers of grippers based on specific network regulations. Taking a novel 6R mechanism as an example, the forward solution of the mechanism is determined, and the relationship between different rotation angles is obtained. Then, displaying the changes in each angle during the grasping process. Finally, the novel 6R and 7R mechanisms are employed as a unit to determine the networking method and assemble new types of grippers. Grippers formed by the aforementioned 1-DOF mechanisms exhibit the characteristics of envelope grasping.

A Coordinate-Free Approach to the Design of Generalized Griffis-Duffy Platforms

Architectural singularity belongs to the Type II singularity, in which a parallel manipulator (PM) gains one or more degrees of freedom and becomes uncontrollable. PMs remaining permanently in a singularity are beneficial for linear-to-rotary motion conversion. Griffis-Duffy (GD) platform is a mobile structure admitting a Bricard motion. In this paper, we present a coordinate-free approach to the design of generalized GD platforms, which consists in determining the shape and attachment of both the moving platform and the fixed base. The generalized GD platform is treated as a combination of six coaxial single-loop mechanisms under the same constraints. Owing to the inversion, hidden in the geometric structure of these single-loop mechanisms, the mapping from a line to a circle establishes the geometric transformation between the fixed base and the moving platform based on the center of inversion, and describes the shape and attachment of the generalized GD platform. Moreover, the center of inversion not only identifies the location of rotation axis, but also affects the shape of the platform mechanism. A graphical construction of generalized GD platforms using inversion, proposed in the paper, provides geometrically feasible solutions of the manipulator design for the requirement of the location of rotation axis.

Design and Reconfiguration Analysis of the Trunk Mechanism for a Reconfigurable Wheeled Mobile Platform

Abstract This paper proposes a reconfigurable wheeled mobile platform (RWMP) consisting of two two-wheeled mobile robots and a reconfigurable trunk. The reconfigurable trunk is a 6R multi-mode single-loop mechanism (SLM) that is obtained by inserting two revolute (R) joints with intersected axes into a planar rhombus 4R mechanism. The 6R mechanism has reconfigurable characteristics owing to changes in the wrench system. All six motion modes and their constraint equations of the 6R mechanism are obtained by solving the closed-loop equation based on the D-H transformation matrix. The analysis shows that the mechanism has six single-DOF motion modes, including a planar rhombus 4R mode, two overconstrained spatial 6R modes, and three coaxial 1R modes. The motion characteristics of the six motion modes are identified using screw theory. The six transition configurations among different modes are identified by combining the constraint equations of each mode. The locomotion modes of the RWMP are designed based on the reconfiguration analysis of the trunk mechanism. The locomotion effect of the RWMP under two confined spaces is verified by simulation analysis and prototype experiment.

Kinematics and Performance Analysis of a Deployable 7R Overconstrained Single-Loop Mechanism for Aerospace Platform

Abstract This paper studies a special deployable 7R single-loop mechanism (SLM), which is characterized by its overconstraints, 1-DOF, and single-loop structure. Based on these characteristics, a series of performance evaluation indices, including the overconstraint performance, input and output motion/force transmission performance, and deploying/folding ratio, are proposed to evaluate its performance. To analyze these performances, the kinematics of the 7R SLM is analyzed. Then, these performance indices are used to evaluate the 7R SLM. The performance analysis result shows that the mechanism exhibits excellent performance. A 3D-printed prototype of the 7R overconstrained SLM is presented and used to assemble a deployable module. Their deploying motion verifies the assembly capability and deployability of the mechanism and its potential as a basic unit to construct more complex, overconstrained deployable mechanisms for aerospace platforms. This study plays a significant role in the analysis, design, and optimization of overconstrained SLMs while also providing theoretical support for applications in aerospace platforms and other related fields.

Structure derivative design, network, and kinematic analysis of a class of two-dimensional deployable mechanisms for aerospace platforms

A systematic method is presented to deal with the structure design of two-dimensional truss-shaped deployable aerospace platforms. Firstly, the DOF, constraints, and singularities of a symmetrical 7R single-loop mechanism (SLM) are analyzed using screw theory. Based on these characteristics, a symmetric double-layer deployable module with one degree of freedom (DOF) is designed by connecting eight 7R SLMs. Taking this deployable module as the parent mechanism, seven homologous deployable modules are derived using the derivative design method. These modules are single DOF and have good symmetry and deployment performance. Then, the networking methods are proposed for planar deployable modules and spatial deployable modules. Using these networking methods, a class of 1-DOF large-scale truss-shaped deployable aerospace platforms with good symmetry and deployment performance are proposed, which verifies the rationality and feasibility of the networking method and design method. Finally, the kinematics and deployment performance of the deployable modules are analyzed. The research fills the gap in the design of deployable aerospace platforms and provides a reference for the derivative design and networking of the deployable mechanisms.

Type synthesis of deployable and symmetrical single-loop mechanisms for constructing aerospace platforms

This paper presents a general synthesis method for 1-DOF single-loop mechanisms (SLMs). This method divides an SLM into two portions: one is a revolute pair and another is a branch chain consisting of several kinematic pairs. The core idea is to design several kinematic pairs in the branch chain without constraining the rotation of the revolute pair. First, the constraint line graph of this revolute pair is drawn. The constraints of the branch chain are classified according to the equivalent constraint line graph of this revolute pair. Subsequently, the synthesis schemes corresponding to these constraints are formulated. Deployable and symmetrical SLMs are constructed, which include not only novel SLMs such as RS1P1RS3RS2P2R, and Rc1Rc2PRc2′Rc1′, but also classical SLMs such as Bennett and Bricard SLMs. It verifies the feasibility and effectiveness of the method. Finally, based on the overconstrained SLMs, another approach for obtaining more deployable non-overconstrained SLMs is proposed. By this approach, some non-overconstrained 7R SLMs are also obtained. Three examples are given to illustrate the potential applications of the obtained SLMs.

Type synthesis of reconfigurable single-loop mechanisms based on planar rhombus mechanisms

This paper deals with the type synthesis of reconfigurable single-loop mechanisms (RSLMs) using screw theory. A novel approach is proposed to synthesize RSLMs by inserting two or four revolute joints to a planar rhombus 4R mechanism. Using the proposed approach, four types of wrench systems of RSLMs are obtained. The reconfiguration analysis of an RSLM with a constraint force system is then carried out using the kinematics close-loop equation and screw theory method. By locking the R joints, it can be found that the mechanism can realize a 1-DOF planar 4R mode, a 1-DOF Bricard mode, a 2-DOF serial mode, a 1-DOF coaxial mode, a 1-DOF Bennett mode, and a 2-DOF spatial 8R mode. Furthermore, four transition configurations among different modes are identified. To verify motion modes of the mechanisms, serval 3D printed models are also presented. This work provides a framework for further study of type synthesis reconfigurable mechanisms from overconstrained single-loop mechanisms.

Structure and function of the ventricular tachycardia isthmus.

Catheter ablation of postinfarction reentrant ventricular tachycardia (VT) has received renewed interest owing to the increased availability of high-resolution electroanatomic mapping systems that can describe the VT circuits in greater detail, and the emergence and need to target noninvasive external beam radioablation. These recent advancements provide optimism for improving the clinical outcome of VT ablation in patients with postinfarction and potentially other scar-related VTs. The combination of analyses gleaned from studies in swine and canine models of postinfarction reentrant VT, and in human studies, suggests the existence of common electroanatomic properties for reentrant VT circuits. Characterizing these properties may be useful for increasing the specificity of substrate mapping techniques and for noninvasive identification to guide ablation. Herein, we describe properties of reentrant VT circuits that may assist in elucidating the mechanisms of onset and maintenance, as well as a means to localize and delineate optimal catheter ablation targets.

Type synthesis of single-loop deployable mechanisms based on improved atlas method for single-DOF grasping manipulators

This paper presents a class of single degree-of-freedom (DOF) grasping manipulators (GMs) with multi-finger design composed of multiple single-loop mechanisms. A method is proposed to type synthesize single-DOF single-loop mechanisms (SLMs) using the improved atlas method. The conventional atlas method produces redundant mechanisms when the diversity of mechanisms is considered; the proposed method addresses this problem. SLM is split into two sub-chains. Sub-chain 1 has only one revolute pair, and one kinematic pair of sub-chain 2 is one revolute pair. Using these two revolute pairs, the type synthesis of SLMs is transformed into the type synthesis of the residual kinematic pairs of sub-chain 2. First, the constraint space of sub-chain 1 is analyzed using screw theory, and the constraint space of sub-chain 2 is further determined and classified. Subsequently, according to the classification of constraints, SLMs are further synthesized using the improved atlas method. Finally, this paper introduces the connection methods for typical SLMs and describes the construction of single-DOF GMs with multi-finger design.

Structure Synthesis and Reconfiguration Analysis of Variable-Degree-of-Freedom Single-Loop Mechanisms With Prismatic Joints Using Dual Quaternions

Abstract This paper deals with the structure synthesis and reconfiguration analysis of variable-DOF (variable-degree-of-freedom) single-loop mechanisms with prismatic joints based on a unified tool—the dual quaternion. According to motion polynomials over dual quaternions, an algebraic method is presented to synthesize variable-DOF single-loop 5R2P mechanisms (R and P denote revolute and prismatic joints, respectively), which are composed of the Bennett and RPRP mechanisms. Using this approach, variable-DOF single-loop RRPRPRR and RRPRRPR mechanisms are constructed by joints obtained from the factorization of motion polynomials. Then reconfiguration analysis of these variable-DOF single-loop mechanisms is performed in light of the kinematic mapping based on dual quaternions as well as the prime decomposition. The results show that the variable-DOF 5R2P mechanisms have a 1DOF spatial 5P2P motion mode and a 2DOF Bennett-RPRP motion mode. Furthermore, the variable-DOF 5R2P mechanisms have two transition configurations, from which the mechanisms can switch among their two motion modes.

A Novel Single-Loop Mechanism and the Associated Cylindrical Deployable Mechanisms

This paper presents a new type of 2-DOF single-loop mechanism inspired by the Sarrus mechanism, and it utilizes this mechanism to construct 2-DOF cylindrical deployable mechanisms. First, the motion pattern of the single-loop mechanism is analyzed utilizing screw theory. According to the structural symmetries, the cylindrical deployable mechanisms are constructed through the linear pattern combination and circular pattern combination of the single-loop mechanisms. After the geometrical analysis and interference condition analysis, the axial, circumferential and area magnification ratios are defined and, furthermore, applied to the parameter optimization of the deployable mechanisms, forming an example surface. Finally, a simplified 1-DOF single-loop mechanism is derived from the proposed 2-DOF mechanism, which is used to construct 1-DOF cylindrical deployable mechanisms with singular free workspaces.

A novel reconfigurable spherical joint based on linear independence of screws and its resultant metamorphic mechanisms

This paper presents a novel reconfigurable spherical (rS) joint resulting from the line dependence of screws and their embodiment geometry. Subsequently, the structure and phase change of the rS joint are elaborated. With this new invention, two novel metamorphic mechanisms, that are, the Schatz-derived metamorphic mechanism and the R(rS)R-R(rS)R metamorphic mechanism, are obtained by inserting the rS joint. The mechanisms entail a reconfiguration process that occurs in two manners: the phase change of the rS joint and the bifurcation of the mechanism. The Schatz-derived metamorphic mechanism entails reconfiguration by phase change of the rS joint and the bifurcation, the R(rS)R-R(rS)R metamorphic mechanism reconfigures the configuration based on phase change of the two rS joints. Remarkably, the former realizes the switch between two assembly configurations without resorting to disassembly and reassembly, and maintains the characteristics of the original Schatz mechanism while the rS joint situates in phase R. The latter changes the mobility and bridges gap between a spatial single-loop mechanism and a structure. With this new reconfigurable joint, various reconfigurable mechanisms could be generated by inserting the reconfigurable joint into the classical ones.

Double loop ventricular tachycardia activation patterns with single loop mechanisms: Asymmetric entrainment responses during "pseudo-figure-of-eight" reentry.

The classical paradigm of scar-related reentrant ventricular tachycardia (VT) features a circuit with a double loop figure-of-eight (F8) activation pattern. The purpose of this study was to interrogate VT circuits with F8 activation patterns by entrainment mapping to differentiate an active loop from a passive loop. Sixty VT circuits with >90% of tachycardia cycle length delineated in high resolution were retrospectively analyzed in 55 patients (nonischemic 49%). A pseudo-F8 VT circuit was defined as a double loop activation pattern driven by a single loop mechanism with a passive loop that yields a long postpacing interval (postpacing interval - tachycardia cycle length ≥ 30 ms). Single loop activation patterns were observed in 33% (n = 20). Of 40 circuits with F8 patterns by activation mapping, 20 were studied with entrainment mapping, where a passive loop was identified by a long postpacing interval in 50%. In 6 circuits where entrainment mapping was performed from both outer loop regions, all demonstrated asymmetric responses to entrainment, confirming a single loop mechanism. Entrainment from both lateral margins of the common pathway (n = 7) demonstrated an asymmetric response in 29%. In all pseudo-F8 circuits (n = 10), the shorter loop functioned as the active loop and ablation targeting the active loop side of the isthmus resulted in VT termination with a single radiofrequency application. In a selected cohort, single loop mechanisms are more prevalent than double loop reentry in reentrant human VT. Half of VT circuits with double loop activation patterns can be demonstrated to be sustained by a single active loop mechanism by entrainment mapping. Ablation targeting the shorter active loop resulted in rapid termination during radiofrequency application.

Accuracy analysis of spatial multi-loop mechanism effected by paired bearings support joint clearance

The primary objective of this work is to present a three-dimensional (3D) clearance model of the paired bearings support joint (PBS-joint) and address the influence of PBS-joint clearance on the accuracy of the spatial multi-loop mechanism. Through the synthetic use of the vector and homogeneous coordinate transformation methods, the 3D clearance model of the PBS-joint is obtained on the basis of the static balance condition. When clearance is equated as a spatial virtual link, the error space solution models of serial mechanism and single-loop mechanism are developed respectively according to the Denavit-Hartenberg method and the geometric closure condition. The error space standardization solution model of the multi-loop mechanism is then presented through improving the low-layer loop sequence description method of the topological structure relations. Finally, the application in the basic loop mechanism is demonstrated to discuss the procedures adopted in this work and the influence of the PBS-joint clearance. Results show that the PBS-joint clearance may cause the error on the point with a 3D deviation transmission path to deviate the normal distribution. Moreover, the plane-joint clearance model may not yield an accurate analysis of the spatial mechanism.

Type Synthesis of Multi-Loop Spatial Mechanisms With Three Translational Output Parameters Based on Virtual-Loop Theory and Assur Groups

SummaryThis paper presents a new approach to synthesize multi-loop mechanisms with three translational displacement parameters based on virtual-loop theory and Assur groups. The approach used kinematic links as a generalized link group added one-by-one to the output link, which further extends the unified link groups in the plane and space. Firstly, the concept of infinitesimal displacement parameters is introduced to describe the displacement parameters. The dependence on the change in the degree of freedom (DOF) and displacement parameters of the output link after adding a 0-DOF generalized link group is established. Then, the link groups with three displacement parameters are synthesized, and the intersection operation rules are given. The single-loop mechanism is synthesized under two circumstances. The 1-, 2-, and 3-DOF dual-loop mechanisms are obtained by adding corresponding generalized link groups. Finally, the multi-loop mechanisms are obtained by adding corresponding generalized link groups. Some novel mechanisms are synthesized to illustrate the effectiveness of the proposed approach.

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.

Uncertainty Analysis of Assembly Error of Planar Single-loop Mechanisms Based on the Rotatability Laws of Linkages

Uncertainty Analysis of Assembly Error of Planar Single-loop Mechanisms Based on the Rotatability Laws of Linkages

Algebraic analysis of overconstrained single loop four link mechanisms with revolute and prismatic joints

Although spatial four link single loop mechanisms with revolute and prismatic joints are well investigated in many publications, there are only few of them dealing with the geometric conditions that cause these generally rigid structures to become movable. This article deals with the derivation of the necessary geometrical design conditions for mobility using kinematic mapping. Furthermore, the coupler motions of the mechanisms are computed. For the Bennett mechanism and the overconstrained RPRP chain the ruled surfaces representing the base surfaces for the line symmetric motions as well as the moving and fixed axodes are computed using the derived design parameters only. All surfaces are computed explicitly and shown in examples. A further contribution of this article is that in case of the RPRP mechanism algebraic mobility conditions in the design parameters are found which have never been published before.

Large deployable network constructed by Altmann linkages

This study proposes a large-scale modular deployable mechanical network constructed by networking Altmann linkages, which are spatial single-loop mechanisms with six revolute joints and four bars, and develops a theoretical approach to verify the feasibility of the networking method. First, the screw motion equation of the linkage is derived, and the deployability of the linkage is demonstrated through a motion simulation. Second, using the overlapping-unit method, a deployable mechanical network is constructed. The constraint graph of the mechanical network is deduced subsequently. The mobility of the mechanical network is proved by screw theory, which demonstrates the feasibility of the networking method. Then, the motion of the mechanical network is simulated and it is found to have excellent deployability. Finally, a prototype of the mechanical network is fabricated. Results show that spatial single-loop linkages can construct modular deployable mechanical networks with the overlapping-unit method under appropriate connections. This networking method can be verified with the theoretical approach proposed in this work.

Optimization of actuating torques in multi-bar prosthetic joints with springs

ABSTRACTThis article presents the optimization of actuating torques in multi-bar prosthetic joints with springs. First, a general model of the planar multi-bar single-loop mechanism with springs for the prosthetic joint is proposed. Secondly, the dynamic matrix of the mechanism is solved by analysing the force condition of a single bar, with the external forces and torques, the forces and torques of the springs as well as the actuating torques being considered. Thirdly, a general optimization method of actuating torques is proposed by taking into account different spring installation situations. Finally, two prosthetic joint examples are presented to show the detailed optimization process, and the effectiveness of the proposed optimization is verified by simulation and experiment. The results prove that the addition of springs in multi-bar prosthetic joints can reduce the absolute values and fluctuations of actuating torques, leading to better energy saving.