Kinematic analysis and singular configurations of a class of parallel robots

1996 ◽  
Vol 41 (3-4) ◽  
pp. 377-390 ◽  
Author(s):  
W. Khalil ◽  
D. Murareci
Keyword(s):  
Kinematic Analysis ◽  
Parallel Robots ◽  
Singular Configurations

Kinematic Analysis and Prototyping of a Partially Decoupled 4-DOF 3T1R Parallel Manipulator

2006 ◽  
Vol 129 (6) ◽  
pp. 611-616 ◽  
Author(s):  
Pierre-Luc Richard ◽  
Clément M. Gosselin ◽  
Xianwen Kong
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Quadratic Equation ◽  
Design Stage ◽  
Forward Displacement ◽  
Singular Configurations ◽  
The Family ◽  
Moving Platform ◽  
Forward Displacement Analysis

A four-degree-of-freedom (DOF) 3T1R parallel manipulator is presented in this paper. This manipulator generates the family of so-called Schönflies motions, SCARA motions or 3T1R motions, in which the moving platform can translate in all directions and rotate around an axis of a fixed direction. The kinematic analysis of this architecture is presented, including the study of the constraint singular configurations, kinematic singular configurations, and the determination of the workspace. A prototype (the Quadrupteron) is also presented and demonstrated. The characteristics of the proposed prototype are (a) there is no constraint singularity, (b) its input-output equations are partially decoupled, (c) its kinematic singular configurations can be expressed using an equation in the angle of rotation of the moving platform and are thus easy to avoid at the design stage, and (d) its forward displacement analysis requires the solution of a univariate quadratic equation and can therefore be solved efficiently.

Tendon Actuated Continuous Structures in Planar Parallel Robots: A Kinematic Analysis

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Sven Lilge ◽  
Kathrin Nuelle ◽  
Georg Boettcher ◽  
Svenja Spindeldreier ◽  
Jessica Burgner-Kahrs
Keyword(s):  
Recent Work ◽  
Constant Curvature ◽  
Kinematic Analysis ◽  
Flexible Structures ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Continuum Robots ◽  
Advantages And Disadvantages ◽  
Reference Design ◽  
Exact Quantification

Abstract The use of continuous and flexible structures instead of rigid links and discrete joints is a growing field of robotics research. Recent work focuses on the inclusion of continuous segments in parallel robots to benefit from their structural advantages, such as a high dexterity and compliance. While some applications and designs of these novel parallel continuum robots have been presented, the field remains largely unexplored. Furthermore, an exact quantification of the kinematic advantages and disadvantages when using continuous structures in parallel robots is yet to be performed. In this paper, planar parallel robot designs using tendon actuated continuum robots instead of rigid links and discrete joints are proposed. Using the well-known 3-RRR manipulator as a reference design, two parallel continuum robots are derived. Inverse and differential kinematics of these designs are modeled using constant curvature assumptions, which can be adapted for other actuation mechanisms than tendons. Their kinematic performances are compared to the conventional parallel robot counterpart. On the basis of this comparison, the advantages and disadvantages of using continuous structures in parallel robots are quantified and analyzed. Results show that parallel continuum robots can be kinematic equivalent and exhibit similar kinematic performances in comparison to conventional parallel robots depending on the chosen design.

Kinematic analysis and self-calibration of three-legged modular parallel robots

1999 ◽  
Author(s):  
Wee K. Lim ◽  
Guilin Yang ◽  
I-Ming Chen ◽  
Song H. Yeo
Keyword(s):  
Kinematic Analysis ◽  
Parallel Robots ◽  
Self Calibration

Kinematic Analysis of a Five-Legged Mobile Robot

2010 ◽  
Author(s):  
Muhammed R. Pac ◽  
Dan O. Popa
Keyword(s):  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Parallel Robot ◽  
Parallel Robots ◽  
The Body ◽  
Legged Robots ◽  
Upper Body ◽  
Design Changes ◽  
Robot Performance ◽  
The Impact

Legged robots are more maneuverable, and can negotiate rough terrain much better than conventional locomotion using wheels. However, since the kinematic or dynamic analysis of such robots involves closed chains, it is typically more difficult to investigate the impact of design changes, such as the number, or the design of its legs, to robot performance. Most legged robots consist of 4 legs (quadrupeds) or 6 legs (hexapods). This paper discusses the kinematic analysis of an unconventional, symmetrical 5-legged robot with 2-DOF (Degrees Of Freedom) universal joints in each leg. The analysis was carried out in order to predict the mobility of the upper body platform, and investigate the number of robot actuators needed for mobility. The product of exponentials formulation with respect to the local coordinate frames is used to describe the twists of the joints. The analysis is based on the idea that the robot body platform along with the legs can be considered instantaneously as a parallel robot manipulating the ground. Hence, the analysis can be done using the Jacobian formulation of parallel robots. Simulation results confirm the mobility analysis that the robot can have at most 3-DOF for the body and that these freedoms are coupled rotations and translations in 3D space also with a dependence on the configuration of the robot.

A new parallel wrist using only revolute pairs: the 3-RUU wrist

Robotica ◽  
2001 ◽  
Vol 19 (3) ◽  
pp. 305-309 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Explicit Form ◽  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Geometric Errors ◽  
End Effector ◽  
Singular Configurations ◽  
Overconstrained Mechanisms ◽  
Three Degrees Of Freedom

Only one parallel wrist with three equal legs containing just revolute pairs has been already presented in the literature. This parallel wrist is overconstrained, i.e., it involves three degrees of freedom required to orientate the end effector by using repetitions of constraints. The overconstrained mechanisms have the drawback of jamming or undergoing high internal loads when geometric errors occur. This paper presents a new parallel wrist, named 3-RUU wrist. The 3-RUU wrist is not overconstrained. It has three equal legs just involving revolute pairs and actuators adjacent to the frame and uses an architecture (3-RUU) already employed to obtain manipulators that make the end effector translate. The 3-RUU wrist kinematic analysis is addressed. This analysis shows that the new parallel wrist can reach singular configurations (translation singularities) in which the spherical constraint between end effector and frame fails. The singularity condition that makes finding all the 3-RUU wrist singular configurations possible is written in explicit form and geometrically interpreted.

Kinematic analysis and path planning of a new kinematically redundant planar parallel manipulator

Robotica ◽  
2008 ◽  
Vol 26 (3) ◽  
pp. 405-413 ◽  
Author(s):  
Iman Ebrahimi ◽  
Juan A. Carretero ◽  
Roger Boudreau
Keyword(s):  
Path Planning ◽  
Condition Number ◽  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Six Degrees Of Freedom ◽  
Displacement Problem ◽  
Singular Configurations ◽  
Planar Parallel Manipulator

SUMMARYIn this work, the 3-RPRR, a new kinematically redundant planar parallel manipulator with six-degrees-of-freedom, is presented. First, the manipulator is introduced and its inverse displacement problem discussed. Then, all types of singularities of the 3-RPRR manipulator are analysed and demonstrated. Thereafter, the dexterous workspace is geometrically obtained and compared with the non-redundant 3-PRR planar parallel manipulator. Finally, based on a geometrical measure of proximity to singular configurations and the condition number of the manipulators' Jacobian matrices, actuation schemes for the manipulators are obtained. Different actuation schemes for a given path are obtained and the quality of their actuation schemes are compared. It is shown that the proposed manipulator is capable of following a path while avoiding the singularities.

Kinematic Analysis and Prototyping of a Partially Decoupled 4-DOF 3T1R Parallel Manipulator

2006 ◽  
Author(s):  
Pierre-Luc Richard ◽  
Cle´ment M. Gosselin ◽  
Xianwen Kong
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Quadratic Equation ◽  
Design Stage ◽  
Forward Displacement ◽  
Singular Configurations ◽  
The Family ◽  
Moving Platform ◽  
Forward Displacement Analysis

A four-degree-of-freedom (DOF) 3T1R parallel manipulator is presented in this paper. This manipulator generates the family of so-called Scho¨nflies motions, SCARA motions or 3T1R motions, in which the moving platform can translate in all directions and rotate around an axis of a fixed direction. The kinematic analysis of this architecture is presented, including the study of the constraint singular configurations, kinematic singular configurations and the determination of the workspace. A prototype (the Quadrupteron) is also presented and demonstrated. The characteristics of the proposed prototype are: (a) there is no constraint singularity, (b) its input-output equations are partially decoupled, (c) its kinematic singular configurations can be expressed using an equation in the angle of rotation of the moving platform and are thus easy to avoid at the design stage, and (d) its forward displacement analysis requires the solution of a univariate quadratic equation and can therefore be solved efficiently.

Six degrees of freedom parallel robots with C5 links

Robotica ◽  
1992 ◽  
Vol 10 (1) ◽  
pp. 35-44 ◽  
Author(s):  
Y. Amirat ◽  
F. Artigue ◽  
J. Pontnau
Keyword(s):  
Automotive Industry ◽  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Parallel Architecture ◽  
Parallel Robot ◽  
Parallel Architectures ◽  
Parallel Robots ◽  
Left Hand ◽  
Six Degrees Of Freedom ◽  
Assembly Tasks

SummaryThis paper presents at first a static and kinematic analysis of closed chains mechanisms which permits to deduce different possible fully parallel architectures. Then we focus on a particular parallel architecture with C5 links designed to perform precise assembly tasks. A general modeling of this C5 parallel robot is presented. Two typical assembly tasks in the automotive industry are also proposed; the first one uses the C5 links parallel robot as a left-hand device, while the second one uses it as the terminal tool of a sequential manipulator.

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