Singular configurations and direct kinematics of a new parallel manipulator

SUMMARYThis work presents the CICABOT, a novel 3-DOF translational parallel manipulator (TPM) with large workspace. The manipulator consists of two 5-bar mechanisms connected by two prismatic joints; the moving platform is on the union of these prismatic joints; each 5-bar mechanism has two legs. The mobility of the proposed mechanism, based on Gogu approach, is also presented. The inverse and direct kinematics are solved from geometric analysis. The manipulator's Jacobian is developed from the vector equation of the robot legs; the singularities can be easily derived from Jacobian matrix. The manipulator workspace is determined from analysis of a 5-bar mechanism; the resulting workspace is the intersection of two hollow cylinders that is much larger than other TPM with similar dimensions.

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Kinematics of a New High-Precision Three-Degree-of-Freedom Parallel Manipulator

Journal of Mechanical Design ◽

10.1115/1.2406103 ◽

2006 ◽

Vol 129 (3) ◽

pp. 320-325 ◽

Cited By ~ 18

Author(s):

Farhad Tahmasebi

Keyword(s):

Power Dissipation ◽

Inverse Kinematics ◽

Parallel Manipulator ◽

Degree Of Freedom ◽

Base Plane ◽

Degree Polynomial ◽

Payload Capacity ◽

Half Angle ◽

Three Degree Of Freedom ◽

Direct Kinematics

Closed-form direct and inverse kinematics of a new three-degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three-DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base mounted, higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of the tangent of the half-angle between one of the limbs and the base plane. Hence, there are at most 16 assembly configurations for the manipulator. In addition, it is shown that the 16 solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

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Jacobian Analysis of a Fully Decoupled Parallel Manipulator for Minimally Invasive Surgery

Volume 4: 36th Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2012-70579 ◽

2012 ◽

Author(s):

Chin-Hsing Kuo ◽

Jian S. Dai

Keyword(s):

Minimally Invasive Surgery ◽

Minimally Invasive ◽

Invasive Surgery ◽

Parallel Manipulator ◽

Jacobian Matrix ◽

Central Point ◽

Special Structure ◽

Jacobian Matrices ◽

Singular Configurations ◽

Reachable Workspace

This paper presents the Jacobian analysis of a parallel manipulator that has a fully decoupled 4-DOF remote center-of-motion for application in minimally invasive surgery. Owing to the special structure of the manipulator, the Jacobian matrix of the manipulator is expressed as a combination of three special Jacobian matrices, namely the Jacobian of motion space, Jacobian of constraints, and Jacobian of actuations. Based on these Jacobian matrices, the singular configurations of the manipulator are then identified. It shows that the configuration singularity only exists at the central point and the boundary of the reachable workspace of the manipulator.

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

Journal of Mechanical Design ◽

10.1115/1.2717611 ◽

2006 ◽

Vol 129 (6) ◽

pp. 611-616 ◽

Cited By ~ 50

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.

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On the Dynamic Properties of Flexible Parallel Manipulators in the Presence of Type 2 Singularities

Journal of Mechanisms and Robotics ◽

10.1115/1.4004229 ◽

2011 ◽

Vol 3 (3) ◽

Cited By ~ 5

Author(s):

Sébastien Briot ◽

Vigen Arakelian

Keyword(s):

Optimal Control ◽

Parallel Manipulator ◽

Dynamic Properties ◽

Parallel Manipulators ◽

Parallel Robot ◽

Inverse Dynamic ◽

Suggested Approach ◽

Singular Configurations ◽

Optimal Force

In the present paper, we expand information about the conditions for passing through Type 2 singular configurations of a parallel manipulator. It is shown that any parallel manipulator can cross the singular configurations via an optimal control permitting the favorable force distribution, i.e., the wrench applied on the end-effector by the legs and external efforts must be reciprocal to the twist along with the direction of the uncontrollable motion. The previous studies have proposed the optimal control conditions for the manipulators with rigid links and flexible actuated joints. The different polynomial laws have been obtained and validated for each examined case. The present study considers the conditions for passing through Type 2 singular configurations for the parallel manipulators with flexible links. By computing the inverse dynamic model of a general flexible parallel robot, the necessary conditions for passing through Type 2 singular configurations are deduced. The suggested approach is illustrated by a 5R parallel manipulator with flexible elements and joints. It is shown that a 16th order polynomial law is necessary for the optimal force generation. The obtained results are validated by numerical simulations carried out using the software ADAMS.

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Kinematics of a New High Precision Three Degree-of-Freedom Parallel Manipulator

Volume 7: 29th Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2005-84059 ◽

2005 ◽

Author(s):

Farhad Tahmasebi

Keyword(s):

Power Dissipation ◽

Inverse Kinematics ◽

Parallel Manipulator ◽

Degree Of Freedom ◽

Base Plane ◽

Degree Polynomial ◽

Payload Capacity ◽

Half Angle ◽

Three Degree Of Freedom ◽

Direct Kinematics

Closed-form direct and inverse kinematics of a new three degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base-mounted; higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of tangent of half-angle between one of the limbs and the base plane. Hence, there are at most sixteen assembly configurations for the manipulator. In addition, it is shown that the sixteen solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

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Improving Motion Stability of the Plane 3-RPR Parallel Manipulator at Singular Configuration

Volume 4A: Dynamics, Vibration, and Control ◽

10.1115/imece2018-86218 ◽

2018 ◽

Author(s):

Yu-Tong Li ◽

Yu-Xin Wang

Keyword(s):

Parallel Manipulator ◽

Parallel Manipulators ◽

Angular Speed ◽

Motion Stability ◽

Singular Configurations ◽

Movable Platform ◽

Singular Configuration ◽

Translation Type ◽

External Forces ◽

Gerschgorin Circle

Kinematic parameters have significant influences on the motion stability of parallel manipulators at singular configureations. Taking the plane 3-RPR parallel manipulator as an example, the motion stability at different types of singular configurations corresponding to the angular speed and velocity of the movable platform are investigated. At first, the second order of uncoupled dynamics equation for the 3-RPR parallel manipulator is established with the aid of the second class Lagrange approach. According to the Lyapunov first approximate stability criterion, the approximate conditions for the 3-RPR parallel manipulator with a stabile motion at singular configurations are determined based on the Gerschgorin circle theorem. Next, the exact Hurwitz criterion is utilized to study the motion stability and the load capability of the manipulator corresponding to the angular speed and velocity of the movable platform, as well as the directions of the external forces at two kinds of singular configurations: with a gained rotation-type DOF, and with a gained translation-type DOF, respectively. The results show that increasing both the angular speed and the velocity of the mass center of the movable platform can efficiently improve the motion stability of the 3-RPR parallel manipulator at singular configurations.

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A new family of spherical parallel manipulators

Robotica ◽

10.1017/s0263574702004174 ◽

2002 ◽

Vol 20 (4) ◽

pp. 353-358 ◽

Cited By ~ 50

Author(s):

Raffaele Di Gregorio

Keyword(s):

Parallel Manipulator ◽

Parallel Manipulators ◽

End Effector ◽

Singular Configurations ◽

New Family ◽

Geometric Conditions ◽

Singularity Locus ◽

The Given ◽

Spherical Parallel Manipulator ◽

Spherical Motion

In the literature, 3-RRPRR architectures were proposed to obtain pure translation manipulators. Moreover, the geometric conditions, which 3-RRPRR architectures must match, in order to make the end-effector (platform) perform infinitesimal (elementary) spherical motion were enunciated. The ability to perform elementary spherical motion is a necessary but not sufficient condition to conclude that the platform is bound to accomplish finite spherical motion, i.e. that the mechanism is a spherical parallel manipulator (parallel wrist). This paper demonstrates that the 3-RRPRR architectures matching the geometric conditions for elementary spherical motion make the platform accomplish finite spherical motion, i.e. they are parallel wrists (3-RRPRR wrist), provided that some singular configurations, named translation singularities, are not reached. Moreover, it shows that 3-RRPRR wrists belong to a family of parallel wrists which share the same analytic expression of the constraints which the legs impose on the platform. Finally, the condition that identifies all the translation singularities of the mechanisms of this family is found and geometrically interpreted. The result of this analysis is that the translation singularity locus can be represented by a surface (singularity surface) in the configuration space of the mechanism. Singularity surfaces drawn by exploiting the given condition are useful tools in designing these wrists.

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