Decoupled and Homokinetic Transmission of Rotational Motion via Constant-Velocity Joints in Closed-Chain Orientational Manipulators

2009 ◽  
Vol 1 (4) ◽  
Author(s):  
Marco Carricato
Keyword(s):  
Constant Velocity ◽  
Design Parameters ◽  
Motor Drive ◽  
Input Output ◽  
End Effector ◽  
Closed Chain ◽  
Constant Velocity Joints ◽  
Kinematic Singularities ◽  
Analytical Expressions ◽  
Derivatives Of

This paper presents novel 2DOF and 3DOF closed-chain orientational manipulators, whose end-effector motion is actuated in a decoupled and homokinetic way by frame-located motors via holonomic transmissions based on constant-velocity couplings. The functioning of these couplings is investigated and the conditions applying for homokinetic transmission to be preserved during simultaneous motor drive are revealed and implemented. As a result, decoupled and configuration-independent relations between the motor rates and the time-derivatives of the variables describing the end-effector orientation are achieved. The attainment of analogous relations between the motor speeds and the components of the end-effector angular velocity is conversely proven to be unfeasible. The problem of singularities is furthermore examined, showing that input-output homokinesis is not a sufficient condition for a globally uniform kinetostatic behavior of the mechanism, which may, indeed, possibly reach uncertainty singular configurations. The connecting chains of the most typical constant-velocity couplings are analyzed, in order to obtain analytical expressions for the functions on which such singularities depend. The influence of design parameters is accordingly inspected. The results are valuable for the type and dimension synthesis of closed-chain wrists free from direct kinematic singularities, and characterized by simple kinematics and regular input-output kinetostatic relations.

Singularity Analysis of Closed Kinematic Chains

1999 ◽  
Vol 121 (1) ◽  
pp. 32-38 ◽  
Author(s):  
F. C. Park ◽  
J. W. Kim
Keyword(s):  
Configuration Space ◽  
Degrees Of Freedom ◽  
Geometric Analysis ◽  
Singularity Analysis ◽  
Geometric Framework ◽  
End Effector ◽  
Kinematic Chains ◽  
Closed Chain ◽  
High Level ◽  
Kinematic Singularities

This paper presents a coordinate-invariant differential geometric analysis of kinematic singularities for closed kinematic chains containing both active and passive joints. Using the geometric framework developed in Park and Kim (1996) for closed chain manipulability analysis, we classify closed chain singularities into three basic types: (i) those corresponding to singular points of the joint configuration space (configuration space singularities), (ii) those induced by the choice of actuated joints (actuator singularities), and (iii) those configurations in which the end-effector loses one or more degrees of freedom of available motion (end-effector singularities). The proposed geometric classification provides a high-level taxonomy for mechanism singularities that is independent of the choice of local coordinates used to describe the kinematics, and includes mechanisms that have more actuators than kinematic degrees of freedom.

A Simplified Design Model for Modular Steel Buildings Subject to Vapor Cloud Explosions (VCEs)

2020 ◽  
Vol 14 ◽  
Author(s):  
Osama Bedair
Keyword(s):  
Dynamic Response ◽  
Minimum Cost ◽  
Design Parameters ◽  
Front Wall ◽  
Steel Buildings ◽  
Element Analysis ◽  
Analysis And Design ◽  
Vapor Cloud ◽  
Building Components ◽  
Analytical Expressions

Background: Modular steel buildings (MSB) are extensively used in petrochemical plants and refineries. Limited guidelines are available in the industry for analysis and design of (MSB) subject to accidental vapor cloud explosions (VCEs). Objectives: The paper presents simplified engineering model for modular steel buildings (MSB) subject to accidental vapor cloud explosions (VCEs) that are extensively used in petrochemical plants and refineries. Method: A Single degree of freedom (SDOF) dynamic model is utilized to simulate the dynamic response of primary building components. Analytical expressions are then provided to compute the dynamic load factors (DLF) for critical building elements. Recommended foundation systems are also proposed to install the modular building with minimum cost. Results: Numerical results are presented to illustrate the dynamic response of (MSB) subject to blast loading. It is shown that (DLF)=1.6 is attained at (td/t)=0.4 for front wall (W1) with (td/T)=1.25. For side walls (DLF)=1.41 and is attained at (td/t)=0.6. Conclusions: The paper presented simplified tools for analysis and design of (MSB) subject accidental vapor cloud blast explosions (VCEs). The analytical expressions can be utilized by practitioners to compute the (MSB) response and identify the design parameters. They are simple to use compared to Finite Element Analysis.

scholarly journals INPUT-OUTPUT RELATION IN A FLEXOR REFLEX

1957 ◽  
Vol 41 (2) ◽  
pp. 297-306 ◽  
Author(s):  
David P. C. Lloyd
Keyword(s):  
Spinal Cord ◽  
Afferent Input ◽  
Surprising Result ◽  
Input Output ◽  
Flexor Reflex ◽  
Afferent Fibers ◽  
Closed Chain ◽  
Central Paths ◽  
Reflex Threshold ◽  
Reflex Discharge

Observations have been made upon a typical flexor reflex with the aim of disclosing the changes in amount, latency, and temporal configuration of reflex discharge that take place as afferent input is varied from zero to maximal for the band of cutaneous myelinated afferent fibers that extends upward from approximately 6 µ in diameter (group II fibers). Reflex threshold is reached at 6 to 12 per cent maximal afferent input. From threshold to maximal input the relation between input and amount of output is essentially linear, latency on the average decreases, the shorter central paths in general gain preference, but the known minimum pathway, one of three neurons, does not transmit unless aided by convergent activity. Flexor reflex discharge may occur in several bursts suggesting the existence of closed chain connections in the internuncial pools of the spinal cord. At any given input there is, in successively elicited reflexes, little correlation between latency and amount of discharge, at first sight a surprising result for each variable can be taken as a measure of excitability status of the motoneuron population. However, latency of discharge indicates excitability at the beginning of the reflex event whereas amount of discharge is an expression of excitability over the entire period of discharge. Given a constantly and rapidly fluctuating excitability absence of correlation between these variables would be an anticipated result.

Analytical Model of the Efficiency of Spur Gears: Study of the Influence of the Design Parameters

2011 ◽  
Author(s):  
Miguel Pleguezuelos ◽  
Jose´ I. Pedrero ◽  
Miryam B. Sa´nchez
Keyword(s):  
Load Distribution ◽  
Gear Ratio ◽  
Design Parameters ◽  
Spur Gears ◽  
Transmitted Power ◽  
Power Losses ◽  
Contact Ratio ◽  
Complete Study ◽  
Uniform Model ◽  
Analytical Expressions

An analytic model to compute the efficiency of spur gears has been developed. It is based on the application of a non-uniform model of load distribution obtained from the minimum elastic potential criterion and a simplified non-uniform model of the friction coefficient along the path of contact. Both conventional and high transverse contact ratio spur gears have been considered. Analytical expressions for the power losses due to friction, for the transmitted power and for the efficiency are presented. From this model, a complete study of the influence of some design parameters (as the number of teeth, the gear ratio, the pressure angle, the addendum modification coefficient, etc.) on the efficiency is presented.

Development of an End-Effector for Mitigation of Collisions

2021 ◽  
Author(s):  
Domenico Tommasino ◽  
Matteo Bottin ◽  
Giulio Cipriani ◽  
Alberto Doria ◽  
Giulio Rosati
Keyword(s):  
Numerical Simulations ◽  
Industrial Applications ◽  
Operating Conditions ◽  
Contact Forces ◽  
Design Parameters ◽  
End Effector ◽  
Linear Behavior ◽  
Stable Mechanism ◽  
Robot Tasks ◽  
The Impact

Abstract In robotics the risk of collisions is present both in industrial applications and in remote handling. If a collision occurs, the impact may damage both the robot and external equipment, which may result in successive imprecise robot tasks or line stops, reducing robot efficiency. As a result, appropriate collision avoidance algorithms should be used or, if it is not possible, the robot must be able to react to impacts reducing the contact forces. For this purpose, this paper focuses on the development of a special end-effector that can withstand impacts and is able to protect the robot from impulsive forces. The novel end-effector is based on a bi-stable mechanism that decouples the dynamics of the end-effector from the dynamics of the robot. The intrinsically non-linear behavior of the end-effector is investigated with the aid of numerical simulations. The effect of design parameters and the operating conditions are analyzed and the interaction between the functioning of the bi-stable mechanism and the control system is studied. In particular, the effect of the mechanism in different scenarios characterized by different robot velocities is shown. Results of numerical simulations assess the validity of the proposed end-effector, which can lead to large reductions in impact forces.

Turret Mooring Design Based on Analytical Expressions of Catastrophes of Slow-Motion Dynamics

1998 ◽  
Vol 120 (3) ◽  
pp. 154-164 ◽  
Author(s):  
M. M. Bernitsas ◽  
L. O. Garza-Rios
Keyword(s):  
Parametric Design ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Slow Motion ◽  
Sensitivity Analyses ◽  
Design Parameters ◽  
Mooring Lines ◽  
The Stability ◽  
Fifth Order ◽  
Analytical Expressions

Analytical expressions of the bifurcation boundaries exhibited by turret mooring systems (TMS), and expressions that define the morphogeneses occurring across boundaries are developed. These expressions provide the necessary means for evaluating the stability of a TMS around an equilibrium position, and constructing catastrophe sets in two or three-dimensional parametric design spaces. Sensitivity analyses of the bifurcation boundaries define the effect of any parameter or group of parameters on the dynamical behavior of the system. These expressions allow the designer to select appropriate values for TMS design parameters without resorting to trial and error. A four-line TMS is used to demonstrate this design methodology. The mathematical model consists of the nonlinear, fifth-order, low-speed, large-drift maneuvering equations. Mooring lines are modeled with submerged catenaries, and include nonlinear drag. External excitation consists of time-independent current, wind, and mean wave drift.

Analytical expressions for gravity anomalies due to homogeneous polyhedral bodies and translations into magnetic anomalies

Geophysics ◽  
1979 ◽  
Vol 44 (4) ◽  
pp. 730-741 ◽  
Author(s):  
M. Okabe
Keyword(s):  
Gravitational Potential ◽  
Computing Time ◽  
Gravity Anomalies ◽  
Magnetic Anomalies ◽  
Two Dimensions ◽  
First Derivative ◽  
Second Derivatives ◽  
Analytical Expressions ◽  
Derivatives Of ◽  
The Magnetic Field

Complete analytical expressions for the first and second derivatives of the gravitational potential in arbitrary directions due to a homogeneous polyhedral body composed of polygonal facets are developed, by applying the divergence theorem definitively. Not only finite but also infinite rectangular prisms then are treated. The gravity anomalies due to a uniform polygon are similarly described in two dimensions. The magnetic potential due to a uniformly magnetized body is directly derived from the first derivative of the gravitational potential in a given direction. The rule for translating the second derivative of the gravitational potential into the magnetic field component is also described. The necessary procedures for practical computer programming are discussed in detail, in order to avoid singularities and to save computing time.

Error estimation and sensitivity analysis of the 3-UPU translational parallel robot due to design parameter uncertainties

2018 ◽  
Vol 233 (8) ◽  
pp. 2713-2727 ◽  
Author(s):  
S El Hraiech ◽  
AH Chebbi ◽  
Z Affi ◽  
L Romdhane
Keyword(s):  
Sensitivity Analysis ◽  
Vertical Axis ◽  
Parallel Robot ◽  
Design Parameters ◽  
Analysis Method ◽  
Parameter Uncertainties ◽  
End Effector ◽  
Interval Analysis Method ◽  
Influential Parameters ◽  
Kinematic Errors

This work deals with the estimation and the sensitivity analysis of the 3-UPU parallel robot error. Based on the Newton–Euler formalism, the robot dynamic model is given in a closed form. This model is validated by the software ADAMS. Using the interval analysis method, a new algorithm is proposed, which estimates the errors in the motion of the end-effector and the errors in the actuator forces as a function of the design parameters uncertainties. The obtained results show that the kinematic errors are minimal at the workspace center. Moreover, these errors increase as the platform moves along the vertical axis. It is also shown that kinematic errors in the actuator joints are the most influential parameters on the manipulator accuracy. Therefore, using actuators with a higher accuracy can highly reduce the errors in motion of the platform.

Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui
Keyword(s):  
Graphical Representation ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
End Effector ◽  
Cartesian Space ◽  
Singularity Locus ◽  
Three Degree Of Freedom ◽  
Analytical Expressions

Abstract In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.

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