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

Direct kinematics and analytical solution to 3RRR parallel planar mechanisms

This paper presents the direct kinematic solutions to 3DOF planar parallel mechanisms. Efforts to solve the direct kinematics of planar parallel mechanisms have concentrated on RPR mechanisms due to its inherent simplicity. It is established that the direct kinematic equations of a general 3DOF planar parallel mechanism can be reduced to a univariate polynomial of degree 8. This paper presents the derivation of this univariate polynomials for both 3RRR and 3RPR mechanisms, showing the similarities and differences between the two common configurations of 3DOF planar parallel mechanisms. This paper also presents the on the direct kinematic solution to a simplified case of the 3RRR planar parallel mechanisms, where it is possible to decouple the polynomial further into two quadratic equations, describing the position and orientation of the end-effector, respectively. This result will provide an efficient computation method for a very useful configuration of planar parallel manipulators

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

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

Pose, posture, formation and contortion in kinematic systems

The concepts of pose, posture, formation and contortion are defined for serial, parallel and hybrid kinematic systems. Workspace and jointspace structure is examined in terms of these concepts. The inter-relationships of pose, posture, formation and contortion are explored for a range of robot workspace and jointspace types

Kinematics, workspace and singularity analysis of a multi-mode parallel robot

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 lock-able 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.Comment: International Design Engineering Technical Conferences \& Computers and Information in Engineering Conference, Aug 2017, Cleveland, United States. 201