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.

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.

A Survey of One Class of 7-Jointed Serially Connected Robots: Type-Synthesis to Obtain Controllably Dexterous Workspace

1989 ◽  
Vol 111 (2) ◽  
pp. 163-175 ◽  
Author(s):  
J. K. Davidson
Keyword(s):  
Screw Theory ◽  
Kinematic Chain ◽  
Synthesis Process ◽  
Geometric Description ◽  
Type Synthesis ◽  
End Effector ◽  
Identification Process ◽  
Kinematic Chains ◽  
Five Axes

A type-synthesis process, which is based on screw theory and geometry, is developed to identify certain robots, each of which can provide controllably dexterous workspace of a tool-point. The identification process is confined to only those robots which control the motion of the end-effector with seven series-connected joints, the axes for the outermost three of which are concurrent. Forty six types of robots are so identified, and, for each, the results are (i) a suitable kinematic chain for the arm and (ii) suitable angle-dimensions for the links of the arm, where the angle-choices are limited to the values 0, ± π/2, and π. A geometric description of the dominant function for control is included. The same kinematic chains are surveyed for all possible parallel and right-angle arrangements of adjacent axes in the four links of the arm. Again utilizing screw theory, 160 robots are identified which do not posses full-cycle axis-dependence among some or all of the first five axes.

Local joint control in cooperating manipulator systems - force distribution and global stability

Robotica ◽  
1993 ◽  
Vol 11 (2) ◽  
pp. 111-118 ◽  
Author(s):  
Greg R. Luecke ◽  
John F. Gardner
Keyword(s):  
Industrial Robot ◽  
Kinematic Chain ◽  
Joint Control ◽  
Constrained Motion ◽  
Computationally Efficient ◽  
Open Chain ◽  
Control Laws ◽  
Kinematic Chains ◽  
Computationally Intensive ◽  
Control Forces

SUMMARYAlmost all industrial robot applications in use today are controlled using a control law that is simple and computationally efficient, local joint error feedback. When two or more open chain manipulators cooperate to manipulate the same object - such as in mechanical grippers, walking machines, and cooperating manipulator systems - closed kinematic chain, redundantly actuated mechanisms are formed. Control approaches for this type of system focus on the more computationally intensive computed torque or inverse plant control laws, due to the concern over instability caused by the unspecified distribution of control forces in the redundant actuator space, and due to the constrained motion caused by the closed kinematic chains.

Synthesis of Planar Mechanisms for Pick and Place Tasks With Guiding Locations

2013 ◽  
Author(s):  
Pierre Larochelle
Keyword(s):  
Algebraic Geometry ◽  
Constraint Equation ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Open Chain ◽  
Synthesis Algorithm ◽  
Kinematic Chains ◽  
Synthesis Technique ◽  
Kinematic Inversion

A novel dimensional synthesis technique for solving the mixed exact and approximate motion synthesis problem for planar RR kinematic chains is presented. The methodology uses an analytic representation of the planar RR dyads rigid body constraint equation in combination with an algebraic geometry formulation of the exact synthesis for three prescribed locations to yield designs that exactly reach the prescribed pick & place locations while approximating an arbitrary number of guiding locations. The result is a dimensional synthesis technique for mixed exact and approximate motion generation for planar RR dyads. A solution dyad may be directly implemented as a 2R open chain or two solution dyads may be combined to form a planar 4R closed chain; also known as a planar four-bar mechanism. The synthesis algorithm utilizes only algebraic geometry and does not require the use of a numerical optimization algorithm or a metric on planar displacements. Two implementations of the synthesis algorithm are presented; computational and graphical construction. Moreover, the kinematic inversion of the algorithm is also included. An example that demonstrates the synthesis technique is included.

Accessibility and Controllability of Flexible Robotic Manipulators

1992 ◽  
Vol 114 (1) ◽  
pp. 50-58 ◽  
Author(s):  
Sabri Tosunoglu ◽  
Shyng-Her Lin ◽  
Delbert Tesar
Keyword(s):  
Case Studies ◽  
System Performance ◽  
Robotic Manipulators ◽  
Joint Space ◽  
Theoretical Framework ◽  
Robotic Systems ◽  
Full System ◽  
Distinct Concept ◽  
Robot Configurations ◽  
The Relationship

Although serial manipulator arms modeled with rigid links show full system controllability in the joint space, this condition does not necessarily hold for flexible robotic systems. In particular, in certain robot configurations, called inaccessible robot positions, one or more of the flexibilities may not be accessed directly by the actuators. This condition may significantly deteriorate system performance as reported earlier by the authors (Tosunoglu et al., 1988, 1989). The present study addresses the relationship between the accessibility and controllability concepts and establishes accessibility as a distinct concept from controllability. Although the theoretical framework is developed for general n-link, spatial manipulators modeled with m oscillation components, example case studies demonstrate the concepts on one- and two-link arms for brevity. Specifically, it is shown that although inaccessibility and uncontrollability may coincide in certain instances (as shown on a one-link arm), counter examples may be found where an arm in an inaccessible position can simultaneously demonstrate full system controllability (as shown on a two-link arm).

Synthesis of 2T1R Decoupled Parallel Manipulators

2011 ◽  
Vol 308-310 ◽  
pp. 2025-2030 ◽  
Author(s):  
Wen Juan Lu ◽  
Li Jie Zhang ◽  
Da Xing Zeng ◽  
Ruo Song Wang
Keyword(s):  
Screw Theory ◽  
Control Design ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Precision Control ◽  
Kinematic Chains ◽  
Step Procedure ◽  
Nonlinear Relation ◽  
Three Degree Of Freedom

For the general parallel mechanisms(PMS), since the coupling between kinematic chains, the nonlinear relation between the input and output is presented, which have led to difficulty in the trajectory planning and precision control. Design of motion decoupled parallel mechanisms(DPMS) has become a good new topic in this area and has captured researcher's attention. In this work, the approach to a synthesis of three degree-of-freedom(3-DOF) DPMS is considered based on screw theory and motion synthesis ideas. Criterions for type synthesis of the branches for DPMS is established according to the twist screw system of the limbs, which assures the decoupling in each limb. Then a six-step procedure is presented for the type synthesis of 2T1R decoupled mechanisms.

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