Spherical Mechanism Research Articles

Using a Point-Line-Plane Representation for Unified Simulation of Planar and Spherical Mechanisms

Abstract This paper presents a geometric constraints driven approach to unified kinematic simulation of n-bar planar and spherical linkage mechanisms consisting of both revolute and prismatic joints. Generalized constraint equations using point, line, and plane coordinates have been proposed which unify simulation of planar and spherical linkages and are demonstrably scalable to spatial mechanisms. As opposed to some of the existing approaches, which seek to derive loop-closure equations for each type of mechanism separately, we have shown that the simulation can be made simpler and more efficient by using unified version of the geometric constraints on joints and links. This is facilitated using homogeneous coordinates and constraints on geometric primitives, such as point, line, and plane. Furthermore, the approach enables simpler programming, real-time computation, and ability to handle any type of planar and spherical mechanism. This work facilitates creation of practical and intuitive design tools for mechanism designers.

RESEARCH OF THE STRESS DISTRIBUTION IN THE HINGE ELEMENT OF THE LEADING RING OF A SPHERICAL TRANSFORMING MECHANISM

The article presents a theoretical study of the stress distribution of the leading links of the spherical transforming mechanism. Diagrams of the stress-strain state and stress fields in the leading element of a spherical mechanism are presented. Methods for improving the reliability and load capacity of the hinge drive shaft with the leading ring of the spherical mechanism are proposed.

FEATURES OF CHOOSING A ROLLING BEARING FOR A SPHERICAL TRANSFORMING MECHANISM

The article presents the rationale for choosing a rolling bearing for a spherical mechanism with two and three degrees of freedom. Calculation schemes for determining the direction and values of active forces are given. Recommendations are given for selecting a rolling bearing based on the forces acting on the mechanism elements.

Developable mechanisms on right conical surfaces

An approach for designing developable mechanisms on a conical surface is presented. By aligning the joint axes of spherical mechanisms to the ruling lines, the links can be created in a way that the mechanism conforms to a conical surface. Terminology is defined for mechanisms mapped onto a right cone. Models are developed to describe the motion of the mechanism with respect to the apex of the cone, and connections are made to cylindrical developable mechanisms using projected angles. The Loop Sum Method is presented as an approach to determine the geometry of the cone to which a given spherical mechanism can be mapped. A method for position analysis is presented to determine the location of any point along the link of a mechanism with respect to the conical geometry. These methods are also applied to multiloop spherical mechanisms.

Design, Analysis, and Test of a Novel 2-DOF Spherical Motion Mechanism

A novel two degree-of-freedom (DOF) ball-joint-like hydraulic spherical motion mechanism (SMM) for use in robotic applications is proposed to achieve smooth spherical motion in all directions. Unlike traditional systems that use serial or parallel mechanisms for generating multi-DOF rotations, the proposed SMM is capable of producing continuous 2-DOF rotational motions in a single joint without intermediate transmission mechanisms. The proposed SMM has a compact structure, low inertia, and high stiffness. First, the architecture and operating principle of the proposed SMM is introduced. Then, the kinematic model is established using Euler transformation, following which factors (such as workspace and dexterity) that have an impact on motion performance are evaluated. As the foundation of dynamics analysis and controller design, the Lagrange’s equations of the second kind are used to establish the dynamic model. To achieve high tracking accuracy, the radial basis function neural network–based sliding mode controller is applied to the mechanism. The simulation results indicate that the designed controller not only improves trajectory tracking capability but also enhances robustness against external disturbance and system uncertainty. Finally, experiments are performed on a prototype SMM to validate the performance of the proposed SMM and evaluate the control method.

基于ANSYS的可重复折展类球面天线支撑机构振动学特性分析

基于ANSYS的可重复折展类球面天线支撑机构振动学特性分析

Design Method and Research of Spherical Radar Calibration Mechanism Based on Positive Pyramid Expandable Unit

Design Method and Research of Spherical Radar Calibration Mechanism Based on Positive Pyramid Expandable Unit

Stability assessment of soil slopes in three dimensions: The effect of the width of failure and of tension crack

This paper investigates the effect of the width of failure and tension crack (TC) on the stability of cohesive-frictional soil slopes in three dimensions. Working analytically, the slip surface and the tension crack are considered to have spheroid and cylindrical shape respectively, although the case of tension crack having planar, vertical surface is also discussed; the latter was found to return higher safety factor values. Because at the initiation of a purely rotational slide along a spheroid surface no shear forces develop inside the failure mass, the rigid body concept is conveniently used; in this respect, the validity of the rigid body concept is discussed, whilst it is supported by comparison examples. Stability tables are given for fully drained and fully saturated slopes without TC, with non-filled TC as well as with fully-filled TC. Among the main findings is that, the width of failure corresponding to the minimum safety factor value is not always infinite, but it is affected by the triggering factor for failure (e.g., water acting as pore pressures and/or as hydrostatic force in the TC). More specifically, it was found that, when a slope is near its limit equilibrium and under the influence of a triggering factor, the minimum safety factor value corresponds to a near spherical failure mechanism, even if the triggering factor (e.g., pore-water pressures) acts uniformly along the third dimension. Moreover, it was found that, the effect of tension crack is much greater when the stability of slopes is studied in three dimensions; indeed, safety factor values comparable to the 2D case are obtained.

Computations analysis of a four-link spherical mechanism for a spatial simulator

Computations analysis of a four-link spherical mechanism for a spatial simulator

A 5-Degrees-of-Freedom Lightweight Elbow-Wrist Exoskeleton for Forearm Fine-Motion Rehabilitation

Exoskeleton robots have been demonstrated to effectively assist the rehabilitation of patients with upper or lower limb disabilities. To make exoskeletons more accessible to patients, they need to be lightweight and compact without major performance tradeoffs. Existing upper limb exoskeletons focus on assistance with coarse motion of the upper arm, whereas forearm fine-motion rehabilitation is often ignored. This paper presents an elbow-wrist exoskeleton with five degrees of freedom (DoFs). Using geared bearings, slider crank mechanisms, and a spherical mechanism for the wrist and elbow modules, this exoskeleton can provide 5-DoF rotary motion forearm assistance. The optimized exoskeleton dimensions allow sufficient rotation output while the motors are placed parallel to the forearm and elbow joint. Thus, compactness and less inertia loading can be achieved. Linear and rotary series elastic actuators with high torque-to-weight ratios are proposed to accurately measure and control interaction force and impedance between exoskeleton and forearm. The resulting 3-kg exoskeleton can be used alone or easily in combination with other exoskeleton robots to provide various robot-aided upper limb rehabilitation.

Development of a Spherical Positioning Robot and Neuro-Navigation System for Precise and Repetitive Non-Invasive Brain Stimulation

Although non-invasive brain stimulation techniques do not involve surgical procedures, the challenge remains in correctly locating the stimulator from outside the head. There is a limit to which one can manually and precisely position and orient the stimulator or repeatedly move the stimulator around the same position. Therefore, in this study, we developed a serial robot with 6 degrees-of-freedom to move the stimulator and a neuro-navigation system to determine the stimulus point from looking at the shape of the subject’s brain. The proposed robot applied a spherical mechanism while considering the safety of the subject, and the workspace of the robot was designed considering the shape of the human head. Position-based visual servoing was applied to compensate for unexpected movements during subject stimulation. We also developed a neuro-navigation system that allows us visually to check the focus of the stimulator and the human brain at the same time and command the robot to the desired point. To verify the system performance, we first performed repeatability and motion compensation experiments of the robot and then evaluated the repeated biosignal response experiments through transcranial magnetic stimulation, a representative technique of non-invasive brain stimulation.

Rigid and Flat Foldability of a Degree-Four Vertex in Origami

AbstractRigid foldability is the property of an origami that folds continuously from an unfolded to a folded state without deformation in its facets. Although extensively researched, there exist no intrinsic conditions for the rigid foldability of a degree-four vertex, which is the simplest possible origami building block that folds nontrivially. In this paper, we derive a necessary and sufficient condition for the rigid foldability of a degree-four vertex and show that it can be reduced to a purely sufficient condition, which is equivalent to a known condition from the realm of spherical mechanisms. The implications of these conditions are discussed, which reveals the connection between rigid and flat foldability, the two most important mathematical notions in origami. In practice, this work further contributes to the design synthesis and analysis of deployable structures, in which the mechanics of degree-four vertices is omnipresent.

Velocity analysis of a spherical parallel robot

A spherical mechanism of parallel structure containing three kinematic chains and performing spherical motions is presented. A distinctive feature of the architecture of the spherical mechanisms is the provision of the constancy of the position of the point – center of rotations. This characteristic causes a wide range of applications of these mechanisms. The kinematic analysis of the mechanism is based on the differentiation of the coupling equations imposed by the kinematic chains. As a result of differentiation, a matrix is obtained by means of which it is possible to solve the direct and inverse problems of kinematics. The velocity analysis is necessary to control the robot and its dynamic analysis.

Use of dual numbers in kinematical analysis of spatial mechanisms. Part I: principle of the method

The general methodology of solving a problem of kinematical analysis of a spatial mechanism is presented. The method is based on the system proposed by Hartenberg and Denavit, concerning the notations of the coordinate frames attached to the elements of the mechanism and on the closure matrix equation of a kinematical chain. Carrying out the closure equation for the case of spherical mechanisms and then applying the transfer principle of Kotelnikov, the equations which allow for finding the unknown parameters of the kinematical chain are obtained. Starting from the typical form of closure equation based on homogenous operators Hartenberg-Denavit, the closure matrix equation is obtained in dual format. By identifying two special matrices it is shown that the coefficient of the dual part from the closure equation is in fact a sum in which each term is attained from the real part of the closure equation by performing simple operations involving the special matrices, that reduce the calculus volume.

Oscillations and control of spherical parallel manipulator

In recent years, there has been a growing number of studies in spherical parallel mechanisms, particularly synthesis, kinematics, and work area singularities. The interaction of degrees of freedom and geometry leads to the nonlinear phenomena, in the dynamics of mechanism. There are few studies into the dynamic properties of such mechanisms. This article deals with the dynamic property of the parallel spherical manipulators, with three degrees of freedom, and presents determination of acceleration input links, oscillations, and the problem of control. Algorithm of control is based on the concept of minimized coordinates, velocities, and acceleration using inverse dynamic problems. This allows synthesis of this algorithm, which can realize a motion in accordance with prescribed trajectories. Finally, the results of calculations are defined.

A compact wrist rehabilitation robot with accurate force/stiffness control and misalignment adaptation

Robots have been demonstrated to assist the rehabilitation of patients with upper or lower limb disabilities. To make exoskeleton robots more friendly and accessible to patients, they need to be lightweight and compact without major performance tradeoffs. Existing upper-limb exoskeleton robots focus on the assistance of the coarse-motion of the upper arm while the fine-motion rehabilitation of the forearm is often ignored. This paper presents a wrist robot with three degrees-of-freedom. Using a geared bearing, slider crank mechanisms, and a spherical mechanism, this robot can provide the complete motion assistance for the forearm. The optimized robot dimensions allow large torque and rotation output while the motors are placed parallel to the forearm. Thus lightweight, compactness, and better inertia properties can be achieved. Linear and rotary series elastic actuators (SEAs) with high torque-to-weight ratios are proposed to accurately measure and control the interaction force and impedance between the robot and the wrist. The resulting 1.5-kg robot can be used alone or easily in combination with other robots to provide various robot-aided upper limb rehabilitation.

Kinematic Calculation of Parallel Link Type Spherical Motion Mechanism using Spherical Trigonometry

Kinematic Calculation of Parallel Link Type Spherical Motion Mechanism using Spherical Trigonometry

Investigation of spherical helix inflatable mechanism for capture of space debris

Investigation of spherical helix inflatable mechanism for capture of space debris

轮-腿复合式移动机器人球面并联腿机构的动力学模型

轮-腿复合式移动机器人球面并联腿机构的动力学模型

ACCURACY OF SPHERICAL MECHANISM

ACCURACY OF SPHERICAL MECHANISM