2,151 research outputs found
The double universal joint wrist on a manipulator: Solution of inverse position kinematics and singularity analysis
This paper presents three methods to solve the inverse position kinematics position problem of the double universal joint attached to a manipulator: (1) an analytical solution for two specific cases; (2) an approximate closed form solution based on ignoring the wrist offset; and (3) an iterative method which repeats closed form position and orientation calculations until the solution is achieved. Several manipulators are used to demonstrate the solution methods: cartesian, cylindrical, spherical, and an anthropomorphic articulated arm, based on the Flight Telerobotic Servicer (FTS) arm. A singularity analysis is presented for the double universal joint wrist attached to the above manipulator arms. While the double universal joint wrist standing alone is singularity-free in orientation, the singularity analysis indicates the presence of coupled position/orientation singularities of the spherical and articulated manipulators with the wrist. The cartesian and cylindrical manipulators with the double universal joint wrist were found to be singularity-free. The methods of this paper can be implemented in a real-time controller for manipulators with the double universal joint wrist. Such mechanically dextrous systems could be used in telerobotic and industrial applications, but further work is required to avoid the singularities
A study of the singularity locus in the joint space of planar parallel manipulators: special focus on cusps and nodes
Cusps and nodes on plane sections of the singularity locus in the joint space
of parallel manipulators play an important role in nonsingular assembly-mode
changing motions. This paper analyses in detail such points, both in the joint
space and in the workspace. It is shown that a cusp (resp. a node) defines a
point of tangency (resp. a crossing point) in the workspace between the
singular curves and the curves associated with the so-called characteristics
surfaces. The study is conducted on a planar 3-RPR manipulator for illustrative
purposes.Comment: 4th International Congress Design and Modeling of Mechanical Systems,
Sousse : Tunisia (2011
Working and Assembly Modes of the Agile Eye
This paper deals with the in-depth kinematic analysis of a special spherical
parallel wrist, called the Agile Eye. The Agile Eye is a three-legged spherical
parallel robot with revolute joints in which all pairs of adjacent joint axes
are orthogonal. Its most peculiar feature, demonstrated in this paper for the
first time, is that its (orientation) workspace is unlimited and flawed only by
six singularity curves (rather than surfaces). Furthermore, these curves
correspond to self-motions of the mobile platform. This paper also demonstrates
that, unlike for any other such complex spatial robots, the four solutions to
the direct kinematics of the Agile Eye (assembly modes) have a simple geometric
relationship with the eight solutions to the inverse kinematics (working
modes)
An Algorithm for Computing Cusp Points in the Joint Space of 3-RPR Parallel Manipulators
This paper presents an algorithm for detecting and computing the cusp points
in the joint space of 3-RPR planar parallel manipulators. In manipulator
kinematics, cusp points are special points, which appear on the singular curves
of the manipulators. The nonsingular change of assembly mode of 3-RPR parallel
manipulators was shown to be associated with the existence of cusp points. At
each of these points, three direct kinematic solutions coincide. In the
literature, a condition for the existence of three coincident direct kinematic
solutions was established, but has never been exploited, because the algebra
involved was too complicated to be solved. The algorithm presented in this
paper solves this equation and detects all the cusp points in the joint space
of these manipulators
Changing Assembly Modes without Passing Parallel Singularities in Non-Cuspidal 3-R\underline{P}R Planar Parallel Robots
This paper demonstrates that any general 3-DOF three-legged planar parallel
robot with extensible legs can change assembly modes without passing through
parallel singularities (configurations where the mobile platform loses its
stiffness). While the results are purely theoretical, this paper questions the
very definition of parallel singularities.Comment: 2nd International Workshop on Fundamental Issues and Future Research
Directions for Parallel Mechanisms and Manipulators, Montpellier : France
(2008
Kinematics and workspace analysis of a 3ppps parallel robot with u-shaped base
This paper presents the kinematic analysis of the 3-PPPS parallel robot with
an equilateral mobile platform and a U-shape base. The proposed design and
appropriate selection of parameters allow to formulate simpler direct and
inverse kinematics for the manipulator under study. The parallel singularities
associated with the manipulator depend only on the orientation of the
end-effector, and thus depend only on the orientation of the end effector. The
quaternion parameters are used to represent the aspects, i.e. the singularity
free regions of the workspace. A cylindrical algebraic decomposition is used to
characterize the workspace and joint space with a low number of cells. The
dis-criminant variety is obtained to describe the boundaries of each cell. With
these simplifications, the 3-PPPS parallel robot with proposed design can be
claimed as the simplest 6 DOF robot, which further makes it useful for the
industrial applications
On the determination of cusp points of 3-R\underline{P}R parallel manipulators
This paper investigates the cuspidal configurations of 3-RPR parallel
manipulators that may appear on their singular surfaces in the joint space.
Cusp points play an important role in the kinematic behavior of parallel
manipulators since they make possible a non-singular change of assembly mode.
In previous works, the cusp points were calculated in sections of the joint
space by solving a 24th-degree polynomial without any proof that this
polynomial was the only one that gives all solutions. The purpose of this study
is to propose a rigorous methodology to determine the cusp points of
3-R\underline{P}R manipulators and to certify that all cusp points are found.
This methodology uses the notion of discriminant varieties and resorts to
Gr\"obner bases for the solutions of systems of equations
Kinematics and Workspace Analysis of a Three-Axis Parallel Manipulator: the Orthoglide
The paper addresses kinematic and geometrical aspects of the Orthoglide, a
three-DOF parallel mechanism. This machine consists of three fixed linear
joints, which are mounted orthogonally, three identical legs and a mobile
platform, which moves in the Cartesian x-y-z space with fixed orientation. New
solutions to solve inverse/direct kinematics are proposed and we perform a
detailed workspace and singularity analysis, taking into account specific joint
limit constraints
Kinematic equations for control of the redundant eight-degree-of-freedom advanced research manipulator 2
The forward position and velocity kinematics for the redundant eight-degree-of-freedom Advanced Research Manipulator 2 (ARM2) are presented. Inverse position and velocity kinematic solutions are also presented. The approach in this paper is to specify two of the unknowns and solve for the remaining six unknowns. Two unknowns can be specified with two restrictions. First, the elbow joint angle and rate cannot be specified because they are known from the end-effector position and velocity. Second, one unknown must be specified from the four-jointed wrist, and the second from joints that translate the wrist, elbow joint excluded. There are eight solutions to the inverse position problem. The inverse velocity solution is unique, assuming the Jacobian matrix is not singular. A discussion of singularities is based on specifying two joint rates and analyzing the reduced Jacobian matrix. When this matrix is singular, the generalized inverse may be used as an alternate solution. Computer simulations were developed to verify the equations. Examples demonstrate agreement between forward and inverse solutions
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