Number Enumeration of Planar Pin-Joined Driving Mechanisms

2011 ◽  
Author(s):  
Peter Mitrouchev ◽  
Fre´de´ric Maffray ◽  
Slim Amri ◽  
Abdelghafour Nafiss ◽  
Marc Dahan
Keyword(s):  
New Method ◽  
Combinatorial Analysis ◽  
End Effector ◽  
Kinematic Chains ◽  
Driving Mechanisms ◽  
Graph Presentation

This paper deals with the development of a new method for the morphological number enumeration for planar pin-jointed driving mechanisms applied in robotic design. The method is based on linkage graph presentation by using geometrical symmetries of kinematic chains and combinatorial analysis. The restricting criteria being the position of: the frame, the end-effector and the actuators (motors) of the robot, different cases of symmetries for planar pin-jointed driving mechanisms of mobility 1 and 2 are addressed. New expressions for calculating the number of different possibilities to position the frame, the end-effector and the actuators in a mechanism are presented, thus reducing the number of the possible solutions by avoiding those that are isomorphic. A further consequence of the present work is the ability for it to be extended to mechanisms with three degrees of mobility and more.

A New Method of Design of Epicyclic Gear Trains

2013 ◽  
Vol 457-458 ◽  
pp. 707-712
Author(s):  
Pei Wen An ◽  
Zhong Liang Lv
Keyword(s):  
New Method ◽  
Combination Method ◽  
Engineering Practice ◽  
Type Number ◽  
Practical Application ◽  
Kinematic Chains ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Number Synthesis ◽  
Method Of Design

Epicyclic gear trains have been broadly applied in engineering practice. In this paper, kinematic chains (K.C.) with single-joint (S.J.) were applied to innovative synthesis of the epicyclic gear trains. The method of the innovative synthesis of the epicyclic gear trains was presented. Not only the epicyclic gear trains in common uses were obtained, but some new types of epicyclic gear trains that are got difficultly by means of conventional combination method were gained. Thereby, a new way has been offered for the innovative synthesis of the epicyclic gear trains, at the same time, a way has also been offered for practical application of some multi-link kinematic chains gained by using the theory of type-number synthesis of the K.C. with S.J.. Examples show that the method presented in this paper is right and feasible, and the method is efficient and practical for the innovative synthesis of the epicyclic gear trains.

A New Method for Detection of Graph Isomorphism Based on the Quadratic Form

2003 ◽  
Vol 125 (3) ◽  
pp. 640-642 ◽  
Author(s):  
P. R. He and ◽  
W. J. Zhang ◽  
Q. Li and ◽  
F. X. Wu
Keyword(s):  
Quadratic Form ◽  
Graph Isomorphism ◽  
New Method ◽  
Eigenvalues And Eigenvectors ◽  
Kinematic Chains ◽  
Quadric Surfaces

This paper proposes a new method for detection of graph isomorphism using the concept of quadratic form. Graphs/kinematic chains are represented first by quadratic form, and the comparison of two graphs is thus reduced to the comparison of two quadratic form expressions. If both the lengths and the directions of the semiaxes of quadric surfaces, which are characterized by the eigenvalues and eigenvectors, are the same, the associated graphs/kinematic chains are isomorphic. An algorithm is developed based on this idea, and tested for the counter-examples known to other methods.

A Synthesis Method for Placing Workpieces in RPR Planar Robotic Workcells in Which Large Rotations Are Required at the Workpiece

1996 ◽  
Author(s):  
K. D. Chaney ◽  
J. K. Davidson
Keyword(s):  
Reference Frame ◽  
Synthesis Method ◽  
Analytical Representation ◽  
New Method ◽  
Two Dimensional ◽  
End Effector ◽  
Radial Location ◽  
Practical Applications ◽  
Full Turn ◽  
Large Rotations

Abstract A new method is developed for determining both a satisfactory location of a workpiece and a suitable mounting-angle of the tool for planar RPR robots that can provide dexterous workspace. The method is an analytical representation of the geometry of the robot and the task, and is particularly well suited to applications in which the task requires large rotations of the end-effector. It is determined that, when the task requires that the end-effector rotate a full turn at just two locations and when the first or third joint in the robot is rotatable by one turn, then the radial location of the workpiece is fixed in the workcell but its angular location is not fixed. When the mounting-angle of the tool is also a variable, the method accommodates tasks in which the tool must rotate a full turn at three locations on the workpiece. The results are presented as coordinates of points in a two-dimensional Cartesian reference frame attached to the workcell. Consequently, a technician or an engineer can determine the location for the workpiece by laying out these coordinates directly in the workcell. Example problems illustrate the method. Practical applications include welding and deposition of adhesives.

scholarly journals On Manipulation of Objects in Three-Fingered Grasp

1995 ◽  
Vol 117 (4) ◽  
pp. 561-565 ◽  
Author(s):  
D. P. Chevallier ◽  
S. Payandeh
Keyword(s):  
Reference Frame ◽  
New Method ◽  
Inner Product ◽  
Product Spaces ◽  
End Effector ◽  
Inner Product Spaces ◽  
Contact Points ◽  
Fixed Reference ◽  
Fine Manipulation

Manipulation of the grasped object is defined as the ability of the mechanical end-effector to create an instantaneous motion of the object with respect to a fixed reference frame (e.g., palm reference frame). This class of manipulation is usually referred to as the fine manipulation whereas a collection of all these instantaneous motions of the object is referred to as the gross manipulation. This paper presents a new method where for a given desired twist of the grasped object, the instantaneous motions of the fingertips can be determined. The results of the paper are divided into two parts. First, for the case where the motion of the object is created through motions of the fingertip in off-tangent planes to the object at the contact points. Second, where a class of motion of the grasped object is achieved through motions of the fingertips which are restricted to the tangent planes. The method of this paper utilizes screw geometry, inner product spaces and information regarding grasp configuration. The method is also illustrated through examples.

Inverse kinematics of free-floating space robots with minimum dynamic disturbance

Robotica ◽  
1996 ◽  
Vol 14 (6) ◽  
pp. 667-675 ◽  
Author(s):  
Fengfeng Xi
Keyword(s):  
Inverse Kinematics ◽  
New Method ◽  
Space Robots ◽  
Simple Fact ◽  
Generalized Jacobian ◽  
Space Manipulator ◽  
End Effector ◽  
Dynamic Disturbance ◽  
Space Manipulators

In this paper a new method is presented for solving the inverse kinematics of free-floating space manipulators. The idea behind the method is to move the space manipulator along a path with minimum dynamic disturbance. The method is proposed to use the manipulator Jacobian instead of the generalized Jacobian of the spacecraft-manipulator system. This is based on the simple fact that, if the space manipulator moves along the so-called Zero Disturbance Path (ZDP), the spacecraft is immovable. As a result, the space manipulator can in this case be treated as a terrestrial fixed-based manipulator. Hence, the motion mapping between the joints and the end-effector can be described directly by the manipulator Jacobian. In the case that the ZDP does not exist, it can be shown that the solutions obtained by the proposed method provide a path with minimum dynamic disturbance.

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.

scholarly journals Polynomial Solution to the Position Analysis of Two Assur Kinematic Chains With Four Loops and the Same Topology

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
Júlia Borràs ◽  
Raffaele Di Gregorio
Keyword(s):  
Polynomial Solution ◽  
Large Family ◽  
The Other ◽  
End Effector ◽  
Closed Loops ◽  
Kinematic Chains ◽  
Position Analysis ◽  
One To One ◽  
Actuated Joints

The direct position analysis (DPA) of a manipulator is the computation of the end-effector poses (positions and orientations) compatible with assigned values of the actuated-joint variables. Assigning the actuated-joint variables corresponds to considering the actuated joints locked, which makes the manipulator a structure. The solutions of the DPA of a manipulator one to one correspond to the assembly modes of the structure that is generated by locking the actuated-joint variables of that manipulator. Determining the assembly modes of a structure means solving the DPA of a large family of manipulators since the same structure can be generated from different manipulators. This paper provides an algorithm that determines all the assembly modes of two structures with the same topology that are generated from two families of mechanisms: one planar and the other spherical. The topology of these structures is constituted of nine links (one quaternary link, four ternary links, and four binary links) connected through 12 revolute pairs to form four closed loops.

A Synthesis Procedure for Design of 3-R Planar Robotic Workcells in Which Large Rotations Are Required at the Workpiece

1992 ◽  
Vol 114 (4) ◽  
pp. 547-558 ◽  
Author(s):  
J. K. Davidson
Keyword(s):  
Motion Planning ◽  
Computer Science ◽  
New Method ◽  
Motion Trajectory ◽  
End Effector ◽  
Radial Location ◽  
Full Turn ◽  
Large Rotations ◽  
Synthesis Procedure ◽  
Planar Robots

A new method is developed for determining both a satisfactory location of a workpiece and a suitable mounting-angle of the tool for planar 3-R robots that can provide dexterous workspace. The method is an adaptation of traditional techniques of linkage synthesis, and it is particularly well-suited to applications in which the motion-trajectory requires large rotations of the end-effector. It is determined that, when the trajectory requires that the end-effector rotate a full turn at just two locations and when the critical joint in the robot is rotatable by one turn, then the radial location of the workpiece is fixed in the workcell but its angular location is not fixed. When the mounting-angle of the tool is also a variable, the method accommodates trajectories in which the tool must rotate a full turn at three locations on the workpiece. The method can be applied not only to planar robots with three hinge-joints, but also to spatial robots, each with a planar 3-R module, when the principal attitudinal excursions of the trajectory are all about a set of parallel axes. Variables are identified, for both the motion-trajectory and the workpiece itself, which strongly affect the design of the workcell and the time for it to complete a motion-trajectory. Example problems illustrate the method. The new method is suggested as an alternative to the existing methods of computer science for motion-planning.

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.

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