Investigation on Kane dynamic equations based on screw theory for open-chain manipulators

2005 ◽  
Vol 26 (5) ◽  
pp. 627-635 ◽  
Author(s):  
Liu Wu-fa ◽  
Gong Zhen-bang ◽  
Wang Qin-que
Keyword(s):  
Screw Theory ◽  
Dynamic Equations ◽  
Open Chain

A Systematical Approach for Structure Synthesis of Parallel Mechanisms Based on Single-Open-Chain Modules and Its Application

2009 ◽  
Author(s):  
Ting-Li Yang ◽  
An-Xin Liu ◽  
Qiong Jin ◽  
Yu-Feng Luo ◽  
Lu-Bin Hang ◽  
...  
Keyword(s):  
Parallel Mechanism ◽  
Systematic Approach ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Open Chain ◽  
Structure Synthesis ◽  
Vector Algebra ◽  
Algebra Theory ◽  
Position And Orientation

Based on previous research results presented by authors, this paper proposes a novel systematic approach for structure synthesis of all parallel mechanisms (excluding Bennett mechanism etc), which is totally different from the approaches based on screw theory and based on displacement subgroup. Main characteristics of this approach are: (a) the synthesized mechanisms are non-instantaneous ones, and (b) only simple mathematical tools (vector algebra, theory of sets, etc.) are used. Main steps of this approach include: (1) Determining functional and structural requirements of the parallel mechanism to be synthesized, such as position and orientation characteristic (POC) matrix, degree of freedom (DOF), etc. (2) Type synthesis of branches. (3) Assembling of branches (determining the geometry constraint conditions among the branches attached between the moving platform and the frame, and checking the DOF). (4) Identifying the inactive joints. (5) Selecting the actuating joints. In order to illustrate the whole procedure, the type synthesis of spherical parallel mechanisms is studied using this approach.

The Geometry of Virtual Work Dynamics in Screw Space

1992 ◽  
Vol 59 (2) ◽  
pp. 411-417 ◽  
Author(s):  
Steven Peterson
Keyword(s):  
Tangent Space ◽  
Screw Theory ◽  
Virtual Work ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Coordinate Space ◽  
Dynamical Equations ◽  
Least Action ◽  
System Of Rigid Bodies ◽  
Configuration Manifold

In this paper, screw theory is employed to develop a method for generating the dynamic equations of a system of rigid bodies. Exterior algebra is used to derive the structure of screw space from projective three space (homogeneous coordinate space). The dynamic equation formulation method is derived from the parametric form of the principle of least action, and it is shown that a set of screws exist which serves as a basis for the tangent space of the configuration manifold. Equations generated using this technique are analogs of Hamilton’s dynamical equations. The freedom screws defining the manifold’s tangent space are determined from the contact geometry of the joint using the virtual coefficient, which is developed from the principle of virtual work. This results in a method that eliminates all differentiation operations required by other virtual work techniques, producing a formulation method based solely on the geometry of the system of rigid bodies. The procedure is applied to the derivation of the dynamic equations for the first three links of the Stanford manipulator.

A Geometric Formulation of Multirotor Aerial Vehicle Dynamics

2021 ◽  
Author(s):  
Youngsuk Hong ◽  
Ramy Rashad ◽  
Soocheol Noh ◽  
Taeyoon Lee ◽  
Stefano Stramigioli ◽  
...  
Keyword(s):  
Lie Group ◽  
Trajectory Optimization ◽  
Screw Theory ◽  
The Body ◽  
Dynamic Equations ◽  
Modeling Framework ◽  
Inertial Parameters ◽  
Rotor Wing ◽  
Aerial Vehicle ◽  
Geometric Formulation

Abstract A geometric dynamic modeling framework for generic multirotor aerial vehicles (MAV), based on a modern Lie group formulation of classical screw theory, is presented. Our framework allows for a broad range of rotor-wing con gurations: any number of rotors can be attached in arbitrary con gurations to either the body or wings, with the rotors and wings also tiltable. Our framework takes into account all masses and inertias of the MAV body and rotors, and accounts for both rotor thrust forces and moments as well as external aerodynamic and other forces. Compared to existing methods, our Lie group framework possesses several practical advantages useful for applications ranging from design optimization to model identi cation and trajectory optimization: (i) the dynamic equations can be easily transformed to coordinates of any reference frame; (ii) kinematic and mass-inertial parameters can be easily factored from the dynamic equations; (iii) exact, closedform analytic derivatives of the dynamics with respect to the con guration variables are easily derived. We demonstrate our systematic modeling procedure on examples of xed-tilt, variable-tilt, and hybrid MAVs with wings.

Dynamic Analysis of a Multi-Rigid-Body Open-Chain System

1983 ◽  
Vol 105 (1) ◽  
pp. 28-34 ◽  
Author(s):  
G. R. Pennock ◽  
A. T. Yang
Keyword(s):  
Rigid Body ◽  
Robot Manipulators ◽  
Dynamic Equations ◽  
Newtonian Mechanics ◽  
Open Chain ◽  
Analytical Technique ◽  
Chain System ◽  
Joint Forces ◽  
Reaction Forces ◽  
Common Effort

In this paper we present an analytical technique, based on Newtonian mechanics with screw calculus and dual-number matrices, to derive the dynamic equations of a multi-rigid-body open-chain system. Next, we outline a systematic procedure to derive closed-form expressions for the joint forces and torques and the reaction forces and moments exerted on each member in the system. Finally, we illustrate the procedure with two examples of robot manipulators. It is hoped that the analytical technique presented here will provide a meaningful alternative, or serve as a complement to existing methods, in our common effort to advance the design of robot manipulators.

Kinematic Analysis Based on Screw Theory of a 3-DOF Cable-Driven Surgical Instrument

2014 ◽  
Vol 490-491 ◽  
pp. 375-378
Author(s):  
Li Min Chang ◽  
Hong Qiang Sang ◽  
Li Ping Xu
Keyword(s):  
Kinematic Analysis ◽  
Screw Theory ◽  
Angular Displacement ◽  
Inverse Kinematic ◽  
Analysis Method ◽  
Surgical Instrument ◽  
Open Chain ◽  
End Effectors ◽  
Forward Kinematic ◽  
And Control

The Forward kinematic and the inverse kinematic were analyzed of 3-DOF cable-driven surgical instrument in this paper. Kinematics of open chain surgical instrument was derived by the product of exponentials formula, and Paden and Kahan subproblems. Kinematic analysis of the 3-DOF cable-driven surgical instrument can be analyzed by the map relationship between the end effectors and the joint angles of the surgical instrument after removal of cables and pulleys and the map relationship between the rotor angular displacement of the motor and joint angular displacement. The analysis method can be useful for motion analysis and control for cable-driven robotic mechanisms.

Kinematic calibration using the product of exponentials formula

Robotica ◽  
1996 ◽  
Vol 14 (4) ◽  
pp. 415-421 ◽  
Author(s):  
Koichiro Okamura ◽  
F.C. Park
Keyword(s):  
Ad Hoc ◽  
Screw Theory ◽  
Geometric Interpretation ◽  
Kinematic Calibration ◽  
Kinematic Parameters ◽  
Open Chain ◽  
Calibration Algorithm ◽  
Forward Kinematic ◽  
Matrix Exponentials ◽  
Derivatives Of

SUMMARYWe present a method for kinematic calibration of open chain mechanisms based on the product of exponentials (POE) formula. The POE formula represents the forward kinematics of an open chain as a product of matrix exponentials, and is based on a modern geometric interpretation of classical screw theory. Unlike the kinematic representations based on the Denavit- Hartenberg (D-H) parameters, the kinematic parameters in the POE formula vary smoothly with changes in the joint axes, ad hoc methods designed to address the inherent singularities in the D-H parameters are therefore unnecessary. Another important advantage is that simple closed-form expressions can be obtained for the derivatives of the forward kinematic equations with respect to the kinematic parameters. After introducing the POE formula, we derive a least-squares kinematic calibration algorithm for general open chain mechanisms. Simulation results with a 6-axis open chain are presented.

A unified approach to mathematical modelling of robotic manipulator dynamics

Robotica ◽  
1994 ◽  
Vol 12 (5) ◽  
pp. 411-420 ◽  
Author(s):  
M.K. Vukobratović ◽  
V.F. Filaretov ◽  
A.I. Korzun
Keyword(s):  
Screw Theory ◽  
Robotic Manipulators ◽  
Unified Approach ◽  
Open Chain ◽  
Kinematic Chains ◽  
Model Derivation ◽  
Direct Problems ◽  
High Degree ◽  
Robot Configurations ◽  
Numerical Complexity

SUMMARYA new method for computer forming of dynamic equations of open-chain mechanical robot configurations is presented. The algorithm used is of a numeric-iterative type, based on mathematical apparatus of screw theory, which has enabled elimination of the unnecessary computations in the process of dynamic model derivation. In addition to conventional kinematic schemes of robotic manipulators, the branched kinematic chains which have recently found their application in the locomotion of robotic mechanisms were also treated. Both the inverse and direct problems of dynamics were addressed. A comparative analysis was carried out of the numerical complexity of various existing algorithms of numeric-iterative type dealing with the problems of spatial active mechanisms dynamics. It has been shown that the proposed method regardless of its generality, approaches by its models complexity symbolic models, which are valid for particular robotic mechanisms only where they achieve a high degree of efficiency.

Automatic Formulation of Dynamic Equations of Motion of Robot Manipulators

1988 ◽  
Vol 202 (6) ◽  
pp. 397-404 ◽  
Author(s):  
D Pan ◽  
R S Sharp
Keyword(s):  
Degrees Of Freedom ◽  
Robot Manipulators ◽  
Equations Of Motion ◽  
Chain Structure ◽  
Algebraic Manipulation ◽  
Dynamic Equations ◽  
Open Chain ◽  
Scalar Form ◽  
Memory Space ◽  
Manipulation Language

Based on the use of homogeneous transformation matrices with Denavit-Hartenberg notation and the Lagrangian formulation method, a general computer program ROBDYN.RED for the symbolic derivation of dynamic equations of motion for robot manipulators has been developed and is discussed in this paper. The program is developed by using REDUCE, an algebraic manipulation language, and is versatile for open-chain structure robot manipulators with any number of degrees of freedom and with any combination of types of joint. Considerations are also given to saving computer memory space required for execution and to minimizing the runtime. Several examples are included to demonstrate the use of the program. Equations of motion in scalar form can be automatically transferred to FORTRAN format for later numerical simulations. The efficiency of the resulting equations in terms of numerical integration is also discussed and some further developments to improve the efficiency are suggested.

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