Analytic formulation of the 6-3 fully-parallel manipulator's singularity determination (original) (raw)
Related papers
Singularity analysis of planar parallel manipulators
Mechanism and Machine Theory, 1995
With regard to planar parallel-manipulators, a general classification of singularities into three groups is introduced. The classification scheme relies on the properties of the Jacobian matrices of the manipulator at hand. The Jacobian matrices of two classes of planar parallel manipulators are derived and the three types of singularities are identified for them. The first class contains 20 manipulators constructed with three different combinations of legs of the PRR, PPR, RRR and RPR types, P and R representing prismatic and revolute pairs, respectively. The second class consists of 4 manipulators constructed with three legs of the PRP and RRP types. Finally, one example for each class is included. Contrary to earlier claims, we show that the third type of singularity is not necessarily architecturedependent.
Instantaneous kinematics and singularity analysis of three-legged parallel manipulators
Robotica, 2004
Instantaneous kinematics and singularity analysis of a class of three-legged, 6-DOF parallel manipulators are addressed in this paper. A generic method of derivation of reciprocal screw and consequently, the instantaneous kinematics model is presented. The advantage of this formulation is that the instantaneous kinematics model possesses well-defined geometric meaning and algebraic structure. Singularity analysis is performed under three categories, namely forward, inverse and combined singularities. A new concept of Passive Joint Plane is introduced to correlate the physical structure of the manipulator and these geometric conditions. In the inverse kinematic analysis, a new approach is introduced. At each leg end point a characteristic parallelepiped is defined whose sides are the linear velocity components from three main joints of the leg. An inverse singularity occurs when the volume of this parallelepiped becomes zero. Examples are demonstrated using RRRS and RPRS-type parallel manipulators.
Singular configurations and direct kinematics of a new parallel manipulator
Proceedings 1992 IEEE International Conference on Robotics and Automation, 1992
We present in this paper a new mechanical architecture for a parallel manipulator. We address the problem of the determination of the singular configurations of this architecture. Then we show that the direct kinematic problem has at most 16 solutions and exhibit an algorithm to find all the solutions.
Mechanism and Machine Theory, 1995
ln this paper, the singularity loci of general three-degree-of-freedom planar parallel manipulators are studied and a graphical representation of these loci in the manipulator's workspace is obtained. The algorithm used here is based on the determination of the roots of the determinant of the manipulator's Jacobian matrix. As mentioned elsewhere, two different types of singularities can occur when parallel manipulators are actuated. Both types are considered here and it is shown that one of the two types leads to a trivial description while the second one is more challenging. On the other hand, architectural singularities are not considered since they are assumed to be eliminated from the outset by a proper choice of the kinematic parameters. Indeed, for the type of manipulator studied here, architectural singularities are very easy to predict and were studied in detail elsewhere. Analytical expressions describing the singularity locus of a planar parallel manipulator are obtained here. Moreover, it is shown that, for a given orientation of the platform, the singularity locus in the plane of motion is a quadratic form, i.e., either a hyperbola, a parabola or an ellipse. Examples illustrating these results are given. For each of these examples, the corresponding singularity locus is graphically superimposed on the manipulator's workspace. This feature has been included in a package developed for the CAD of parallel manipulators. Cases of manipulators for which the singularity locus is located outside of the workspace for certain orientations of the platform are presented. Additionally, three-dimensional representions of the singularity loci are given. The graphical representation of the singularity loci is a very powerful design tool which can be of great help, especially in the context of parallel manipulators.
Singularity Analysis of a 3-PRRR Kinematically Redundant Planar Parallel Manipulator
Journal of Mechanical Engineering, 2010
Finding Singular configurations (singularities) is one of the mandatory steps during the design and control of mechanisms. Because, in these configurations, the instantaneous kinematics is locally undetermined that causes serious problems both to static behavior and to motion control of the mechanism. This paper addresses the problem of determining singularities of a 3-PRRR kinematically redundant planar parallel manipulator by use of an analytic technique. The technique leads to an input -output relationship that can be used to find all types of singularities occurring in this type of manipulators.
Singularity Conditions of 3T1R Parallel Manipulators With Identical Limb Structures
Journal of Mechanisms and Robotics, 2012
This paper deals with the singularity analysis of parallel manipulators with identical limb structures performing Schönflies motions, namely, three independent translations and one rotation about an axis of fixed direction (3T1R). Eleven architectures obtained from a recent type synthesis of such manipulators are analyzed. The constraint analysis shows that these architectures are all overconstrained and share some common properties between the actuation and the constraint wrenches. The singularities of such manipulators are examined through the singularity analysis of the 4-RUU parallel manipulator. A wrench graph representing the constraint wrenches and the actuation forces of the manipulator is introduced to formulate its superbracket. Grassmann–Cayley Algebra is used to obtain geometric singularity conditions. Based on the concept of wrench graph, Grassmann geometry is used to show the rank deficiency of the Jacobian matrix for the singularity conditions. Finally, this paper sho...
Singularity Analysis of a 3DOF Parallel Manipulator Using Infinite Constraint Plane Method
Journal of Intelligent and Robotic Systems, 2008
In this article a novel geometrical method is presented to obtain singular points of a parallel manipulator. First, the constrained plain method (CPM) and some of its application in parallel mechanism is introduced. Given the definition of constraint plane (CP) and infinite constraint plane (ICP) the dependency conditions of constraints is achieved with the use of a new theorem based on the Ceva geometrical theorem. Another theorem is used to achieve the direction of angular velocity of a body having three ICPs. Finally, as an example, using these two theorems, singularities of the 3UPS_PU mechanism are obtained. This method is completely geometrical, involving no complex or massive calculations and yields the answer quickly. In the previous methods based on the Grassmann geometry, the mechanism needs to be statically analyzed at first, so that the Inverse Jacobian matrix is achieved, and then the Plucker-vector is derived. It usually needs exhaustive search of the workspace using an accurate analytical model of the mechanism kinematics and may lead to plenty of conditions remained to be pondered in order to obtain the singularity conditions.
Singularity analysis of CaPaMan: a three-degree of freedom spatial parallel manipulator
Robotics and Automation, …, 2001
CaPaMan (Cassino Parallel Manipulator) is a threedegree of freedom parallel mechanism that has been designed and built at Laboratory of Robotics and Mechatronics in Cassino. In this paper a study of the configuration singularities of the CaPaMan manipulator is presented by considering two different methods: an algebraic formulation and a vector analysis. It will be shown that a formulation can give singularity related to the failure of the kinematic model at particular configurations of the manipulator. It will also be proved that this type of singularity can be avoided by a proper analysis of the problem.
A novel criterion for singularity analysis of parallel mechanisms
Mechanism and Machine Theory, 2019
A novel criterion for singularity analysis of parallel robots is presented. It relies on screw theory, the 3-dimensional Kennedy theorem, and the singular properties of minimal parallel robots. A parallel robot is minimal if in any generic configuration, activating any leg/limb causes a motion in all its joints and links. For any link of the robot, a pair of legs is removed. In the resulting 2 degrees-of-freedom mechanism, all possible instantaneous screw axes belong to a cylindroid. A center axis of this cylindroid is determined. This algorithm is performed for three different pairs of legs. The position is singular, if the instantaneous screw axis of the chosen link crosses and is perpendicular to three center axes of the cylindroids. This criterion is applied to a 6/6 Stewart Platform and validated on a 3/6 Stewart Platform using results known in the literature. It is also applied to two-platform minimal parallel robots and verified through the Jacobian; hence demonstrating its general applicability to minimal robots. Since any parallel robot is decomposable into minimal robots, the criterion applies to all constrained parallel mechanisms.