Kinematic Analysis of HALF Parallel Robot

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...

Mechanism and Machine Theory, 2009

An efficient approach for determining the force-unconstrained poses (singularity loci) of planar parallel manipulators (PPMs) is presented. The approach is implemented for the 3-RPR, 3-PRR, and 3-RRR PPMs, where the underline indicates the actuated joint. The force-unconstrained poses are identified based upon concepts of reciprocal screws, kinematics, and elimination methods. The use of screw quantities provides a clear insight as to how the forces are acting on the mechanism. This allows finding conditions of singular configurations that are related to displacements of passive joints. Based on these conditions, the force-unconstrained poses are obtained by solving the forward kinematic analysis of manipulators with the same architecture but different actuation layouts. It is demonstrated that the singularity loci of the 3-RPR, 3-PRR, and 3-RRR PPMs can be described with single-variable polynomials of degrees 2, 2, and 6, respectively. j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / m e c h m t

Serial and Parallel Robot Manipulators - Kinematics, Dynamics, Control and Optimization, 2012

2009

While a number of researchers have published results in the area of parallel robot singularity determination and the a posteriori elimination of these singularities, far less work has been published in the area of singularity free workspace design. Several researchers have committed substantial funds to design hardware prototypes that have proven worthless because of unavoidable singularities. This trend, if carried over to industrial applications, could prove especially detrimental to the future of applied parallel robotics. A comprehensive and straightforward design strategy that guarantees a singularity free workspace is presented in this paper. The design problem is mathematically modeled, and relaxations are suggested for finding solutions. The translational 3-UPU parallel robot is studied to verify the efficacy of the design approach.

IEEE Transactions on Automation Science and Engineering, 2001

In this paper, a new spatial three-degrees-of-freedom (two degrees of translational freedom and one degree of rotational freedom) parallel manipulator is proposed. The parallel manipulator consists of a base plate, a movable platform, and three connecting legs. The inverse and forward kinematics problems are described in closed forms and the velocity equation of the new parallel manipulator is given. Three kinds of singularities are also presented. The workspace for the manipulator is analyzed systematically; in particular, indices to evaluate the mobility (in this paper, mobility means rotational capability) of the moving platform of the manipulator will be defined and discussed in detail. Finally, a topology architecture of the manipulator is introduced. The parallel manipulator has wide application in the fields of industrial robots, simulators, micromanipulators, and parallel machine tools.

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.

2012 Third International Conference on Digital Manufacturing & Automation, 2012

A novel asymmetrical spatial parallel robotic manipulator with three degrees of freedom (DOF) is proposed. The moving platform of the mechanism has two-translational and one-rotational DOF with respect to the fixed base. Motion output characteristics and the mobility of the manipulator are analyzed based on the screw theory. Solutions of position and velocity for both direct and inverse kinematics are derived. Furthermore, the singularity and the dexterity are discussed. The Jacobian matrix, mapping the input velocity vector space of the actuated joints into the output velocity vector space of the moving platfomr, is an identical 3 3 matrix, so the parallel mechanism is a free-singularity fully-isotropic one. Thus, this mechanism performs very well with regard to motion and force transmission and has potential applications in the field of industrial robots and medical devices.

arXiv (Cornell University), 2017

A family of reconfigurable parallel robots can change motion modes by passing through constraint singularities by locking and releasing some passive joints of the robot. This paper is about the kinematics, the workspace and singularity analysis of a 3-PRPiR parallel robot involving lockable Pi and R (revolute) joints. Here a Pi joint may act as a 1-DOF planar parallelogram if its lockable P (prismatic) joint is locked or a 2-DOF RR serial chain if its lockable P joint is released. The operation modes of the robot include a 3T operation modes to three 2T1R operation modes with two different directions of the rotation axis of the moving platform. The inverse kinematics and forward kinematics of the robot in each operation modes are dealt with in detail. The workspace analysis of the robot allow us to know the regions of the workspace that the robot can reach in each operation mode. A prototype built at Heriot-Watt University is used to illustrate the results of this work.

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. 1. Singularity of type I: occurs when matrix B is singular 2. Singularity of type II: occurs when matrix A is singular 3. Singularity of type III: occurs when the nonlinear kinematic constraints degenerate.

Mechanism and Machine Theory, 2019

A three-dof 2PUR-2RPU redundantly-actuated parallel-kinematics machine, designed for the machining of complex curved surfaces that requires high-speed and high-precision, is the object of study in this report. The lower-mobility PKM, consisting of two pairs of symmetric, limited-dof limbs, has the advantages of high stiffness, simple kinematic chain, and reduced singularities. The mobility of the robot is investigated via Lie-groups, instead of the well-known Chebyshev-Grübler-Kutzbach formulas, which are not applicable to our case. Then, the inverse-displacement, direct-displacement and corresponding velocity relations are analyzed in detail. Next, by investigating the rank-deficiency of the corresponding Jacobian, three types of singularities, those associated with direct-kinematics, inverse-kinematics and combinations thereof, are analyzed in depth, while constraint singularities are investigated by resorting to constraint wrenches. Moreover, the workspace of both the operation point P and the tool head, when a tool is added to the moving platform, are derived. It is noteworthy that the local and global dexterity indices are evaluated by resorting to the characteristic length to homogenize the dimensionally inhomogeneous Jacobian matrix at hand, then by gradient optimization to solve the minimum-condition-number problem.