A General Method for Kinematic Analysis of Robotic Wrist Mechanisms

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Ilie Talpasanu
Keyword(s):  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Simple Procedure ◽  
Efficient Computation ◽  
General Applicability ◽  
Cycle Basis ◽  
Angular Velocities ◽  
Gear Trains ◽  
Cycle Matroid ◽  
Robotic Wrist

Abstract The paper presents a novel and simple technique for the kinematic analysis of bevel gear trains (BGT). The approach is based on edge-oriented graphs for efficient computation of BGT’s absolute and relative velocities of links using incidence matrices. The kinematic equations are generated in matrix form using a cycle basis from a cycle matroid. The set of independent equations is automatically obtained from matrix orthogonalities and not by taking derivatives. Equation coefficients are expressed as function of speed ratios and have minimal variables. Then the relationships between the output and input angular velocities can be determined. In addition, a simple procedure is demonstrated to check for mechanism singularities. The method presented here has general applicability and can be employed for spatial geared mechanisms with any number of gears and degrees of freedom (DOF) as illustrated by numerical examples of robotic wrist mechanisms.

A General Method for Kinematic Analysis of Epicyclic Bevel Gear Trains Applied to Robotic Wrist Mechanisms

2013 ◽  
Author(s):  
Ilie Talpasanu
Keyword(s):  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Simple Procedure ◽  
Bevel Gear ◽  
Efficient Computation ◽  
General Applicability ◽  
Cycle Basis ◽  
Angular Velocities ◽  
Gear Trains ◽  
Robotic Wrist

This paper presents a novel and simple technique for the kinematic analysis of bevel gear trains (BGT). The approach is based on edge-oriented graphs for efficient computation of BGT’s relative and absolute velocities of links using incidence matrices. The kinematic equations are generated in matrix form using a cycle basis from a cycle matroid. The set of independent equations is automatically obtained from matrix orthogonalities and not by taking derivatives. Equation coefficients are expressed as function of speed ratios and have minimal variables. Then the relationships between the output and input angular velocities can be determined. In addition, a simple procedure is demonstrated to check for mechanism singularities. The method presented here has general applicability and can be employed for spatial geared mechanisms with any number of gears and degrees of freedom as illustrated by numerical examples of robotic wrist mechanisms.

Kinematic Analysis of Epicyclic Bevel Gear Trains With Matroid Method

2012 ◽  
Vol 134 (11) ◽  
Author(s):  
Ilie Talpasanu ◽  
P. A. Simionescu
Keyword(s):  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Time Derivative ◽  
Oriented Graph ◽  
Bevel Gear ◽  
Efficient Computation ◽  
Cycle Basis ◽  
Angular Velocities ◽  
Gear Trains ◽  
Cycle Matroid

The paper presents a novel technique for the kinematic analysis of bevel gear trains using the incidence matrices of an edge-oriented graph of the mechanism. The kinematic equations are then obtained in matrix form using a cycle basis from a cycle matroid. These equations can be systematically generated, and allow for an efficient computation of the angular velocities of the gears and planet carriers of the mechanism without employing time derivative operations. As illustrated in the paper, the method is applicable to bevel gear trains of any number of gears or degrees of freedom.

Application of Matroid Method in Kinematic Analysis of Parallel Axes Epicyclic Gear Trains

2006 ◽  
Vol 128 (6) ◽  
pp. 1307-1314 ◽  
Author(s):  
Ilie Talpasanu ◽  
T. C. Yih ◽  
P. A. Simionescu
Keyword(s):  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Oriented Graph ◽  
General Applicability ◽  
Epicyclic Gear ◽  
Angular Velocities ◽  
Gear Trains ◽  
Transfer Method ◽  
Cycle Matroid ◽  
Mobile Links

A novel method for kinematic analysis of parallel-axes epicyclic gear trains is presented, called the incidence and transfer method, which uses the incidence matrices associated with the edge-oriented graph associated to the mechanism and the transfer joints (teeth contact joints). Relative to such joints, a set of independent equations can be generated for calculating the angular positions, velocities, and accelerations. Complete kinematic equations are obtained in matrix form using a base of circuits from a cycle matroid. The analysis uses the relationships between the number of mobile links, number of joints, and number of circuits in the base of circuits, together with the Latin matrix (whose entries are function of the absolute values of the partial gear ratios of the transmission). Calculating the rank of the Latin matrix can identify singularities, like groups of gears that rotate as a whole. Relationships between the output and input angular velocities and accelerations are then determined in a matrix-based approach without using any derivative operations. The proposed method has general applicability and can be employed for systems with any number of gears and degrees of freedom, as illustrated by the numerical examples presented.

Simplified Kinematic Analysis of Bevel Epicyclic Gear Trains With Application to Power-Flow and Efficiency Analyses

2005 ◽  
Vol 127 (2) ◽  
pp. 278-286 ◽  
Author(s):  
Carl A. Nelson ◽  
Raymond J. Cipra
Keyword(s):  
Graph Theory ◽  
Kinematic Analysis ◽  
Power Flow ◽  
Computer Software ◽  
Input And Output ◽  
Automatic Transmissions ◽  
Epicyclic Gear ◽  
Analysis Technique ◽  
Angular Velocities ◽  
Gear Trains

A kinematic analysis technique is introduced to find the angular velocities of all links in bevel epicyclic gear trains. The method relies on previous work in graph theory. It improves on existing techniques used for analysis of planar geared mechanisms in its ability to accurately solve the kinematics of spatial geared mechanisms, particularly bevel gear trains, in a simpler manner. Usefulness of the method is demonstrated through its application to power-flow and efficiency analyses as well as its implementation in computer software. This discussion is limited to gear trains whose input and output axes are collinear, such as automotive automatic transmissions.

Lumped Parameter Model of Planetary Gear Systems

1978 ◽  
Vol 192 (1) ◽  
pp. 251-258 ◽  
Author(s):  
J. W. Polder
Keyword(s):  
Degrees Of Freedom ◽  
Planetary Gear ◽  
Lumped Parameter Model ◽  
Damping Coefficients ◽  
Planetary Gear Trains ◽  
Lumped Parameter ◽  
Vibration Model ◽  
Close Relationship ◽  
Angular Velocities ◽  
Gear Trains

A model system is described by parameters for shafts, planetary gear trains and nodes. Moments of inertia, spring stiffnesses and damping coefficients are assigned to the shafts; gear ratios and efficiencies are assigned to planetary gear trains. The equivalence of angular velocities and torques is demonstrated for shafts (vibration model), as well as for planetary gear trains and nodes (configuration of the system). This brings about a new view on the concept of degrees of freedom. The close relationship between gear ratios and torque ratios yields identical functions for these ratios when applied to the input and output shafts of a system. The full use of this relationship requires strict conventions of signs and an extension of the interpretation of values. The introduction of a new concept, named responsivity, expresses the relationships between torques and between powers of arbitrary shafts. With suitable equations, it becomes possible to investigate torque and power distributions exhaustively.

A New Graph Representation for the Automatic Kinematic Analysis of Planetary Spur-Gear Trains

1992 ◽  
Vol 114 (1) ◽  
pp. 196-200 ◽  
Author(s):  
Cheng-Ho Hsu ◽  
Kin-Tak Lam
Keyword(s):  
Computer Program ◽  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Spur Gear ◽  
Gear Train ◽  
Graph Representation ◽  
Kinematic Structure ◽  
Rotational Displacement ◽  
Interactive Computer Program ◽  
Gear Trains

The purpose of this paper is to propose a new graph representation to represent the kinematic structure of a planetary spur-gear train efficiently. Based on the graph representation, the kinematic analysis of planetary spur-gear trains is largely simplified. An interactive computer program is developed for the kinematic analysis of planetary spur-gear trains with any number of degrees of freedom. By only inputting the graph representation of a planetary spur-gear train and the data for the mating gear pairs, all possible fundamental circuits are determined and the rotational displacement equations are derived and solved automatically.

A New Graph Representation for the Automatic Kinematic Analysis of Planetary Spur-Gear Trains

1989 ◽  
Author(s):  
C.-H. Hsu ◽  
K. T. Lam
Keyword(s):  
Computer Program ◽  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Spur Gear ◽  
Gear Train ◽  
Graph Representation ◽  
Kinematic Structure ◽  
Rotational Displacement ◽  
Interactive Computer Program ◽  
Gear Trains

Abstract The purpose of this paper is to propose a new graph representation to represent the kinematic structure of a planetary spur-gear train efficiently. Based on the graph representation, the kinematic analysis of planetary spur-gear trains is largely simplified. An interactive computer program is developed for the kinematic analysis of planetary spur-gear trains with any numbers of degrees of freedom. By only inputting the graph representation of a planetary spur-gear trains and the data of the mating gear pairs, all possible fundamental circuits are determined and the rotational displacement equations are derived and solved automatically.

scholarly journals Development of Non Expensive Technologies for Precise Maneuvering of Completely Autonomous Unmanned Aerial Vehicles

Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 391
Author(s):  
Luca Bigazzi ◽  
Stefano Gherardini ◽  
Giacomo Innocenti ◽  
Michele Basso
Keyword(s):  
Unmanned Aerial Vehicles ◽  
Degrees Of Freedom ◽  
Vision System ◽  
Video Stream ◽  
Measurement Unit ◽  
Absolute Position ◽  
Light Load ◽  
Aerial Vehicles ◽  
Angular Velocities ◽  
Custom Hardware

In this paper, solutions for precise maneuvering of an autonomous small (e.g., 350-class) Unmanned Aerial Vehicles (UAVs) are designed and implemented from smart modifications of non expensive mass market technologies. The considered class of vehicles suffers from light load, and, therefore, only a limited amount of sensors and computing devices can be installed on-board. Then, to make the prototype capable of moving autonomously along a fixed trajectory, a “cyber-pilot”, able on demand to replace the human operator, has been implemented on an embedded control board. This cyber-pilot overrides the commands thanks to a custom hardware signal mixer. The drone is able to localize itself in the environment without ground assistance by using a camera possibly mounted on a 3 Degrees Of Freedom (DOF) gimbal suspension. A computer vision system elaborates the video stream pointing out land markers with known absolute position and orientation. This information is fused with accelerations from a 6-DOF Inertial Measurement Unit (IMU) to generate a “virtual sensor” which provides refined estimates of the pose, the absolute position, the speed and the angular velocities of the drone. Due to the importance of this sensor, several fusion strategies have been investigated. The resulting data are, finally, fed to a control algorithm featuring a number of uncoupled digital PID controllers which work to bring to zero the displacement from the desired trajectory.

Three-dimensional asymmetric maximum weight lifting prediction considering dynamic joint strength

2021 ◽  
pp. 095441192098703
Author(s):  
Rahid Zaman ◽  
Yujiang Xiang ◽  
Jazmin Cruz ◽  
James Yang
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Three Dimensional ◽  
Optimization Method ◽  
Weight Lifting ◽  
Joint Torque ◽  
Maximum Weight ◽  
Angular Velocities ◽  
Asymmetric Lifting

In this study, the three-dimensional (3D) asymmetric maximum weight lifting is predicted using an inverse-dynamics-based optimization method considering dynamic joint torque limits. The dynamic joint torque limits are functions of joint angles and angular velocities, and imposed on the hip, knee, ankle, wrist, elbow, shoulder, and lumbar spine joints. The 3D model has 40 degrees of freedom (DOFs) including 34 physical revolute joints and 6 global joints. A multi-objective optimization (MOO) problem is solved by simultaneously maximizing box weight and minimizing the sum of joint torque squares. A total of 12 male subjects were recruited to conduct maximum weight box lifting using squat-lifting strategy. Finally, the predicted lifting motion, ground reaction forces, and maximum lifting weight are validated with the experimental data. The prediction results agree well with the experimental data and the model’s predictive capability is demonstrated. This is the first study that uses MOO to predict maximum lifting weight and 3D asymmetric lifting motion while considering dynamic joint torque limits. The proposed method has the potential to prevent individuals’ risk of injury for lifting.

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