Forward Kinematic Singularity Research Articles

Kinematic analysis and optimal design of a novel 3-PRR spherical parallel manipulator

This paper introduces a novel three degree-of-freedom spherical parallel manipulator with 3-PRR topology, where P and R denote a curved prismatic joint and a revolute joint, respectively. The first revolute joint of each PRR leg is actuated via a double Rzeppa-type driveshaft, and hence underlined. The manipulator has at most eight working modes and eight assembly modes. However, only one working mode and one assembly mode of the manipulator are acceptable during its motion which can be easily identified. Singularity and kinematic dexterity analyses reveal that the proposed 3-PRR spherical parallel manipulator has no forward kinematic singularity for a wide range of rotation of the moving platform around its central axis. An optimal design of the manipulator is also presented having a workspace with good kinematic dexterity.

Kinematics, workspace and optimal design of a novel 4RSS + PS parallel manipulator

In this paper, a novel four degrees of freedom (DOFs) parallel manipulator (PM) is introduced and its kinematics, workspace and optimal design are systematically studied. The manipulator is called 4RSS + PS PM having four active RSS type legs and one passive PS type leg. R, S and P stand for revolute, spherical and prismatic joints, respectively, and R denotes the actuated revolute joints. Moving platform of the manipulator has three rotational motions along with one translational motion (3R1T). As an advantage, rotational motion of the moving platform around the axis of its translational motion has no limitation. This makes the manipulator so suitable for machining applications in holes, cylinders and so on. Closed form solutions are found for the inverse and forward position kinematics problems of the manipulator. The manipulator workspace is determined numerically in a 3D space. A special design of the manipulator free of inverse and forward kinematic singularities is specified. Kinematic dexterity analysis is carried out based on the condition number of the manipulator Jacobian matrix showing that the manipulator has no singularity inside the workspace. Two architecture optimizations are also presented to achieve a maximum workspace volume of the manipulator, and to find a workspace with a desired value of kinematic dexterity.

Higher-Order Analysis of Kinematic Singularities of Lower Pair Linkages and Serial Manipulators

Kinematic singularities of linkages are configurations where the differential mobility changes. Constraint singularities are critical points of the constraint mapping defining the loop closure constraints. Configuration space (c-space) singularities are points where the c-space ceases to be a smooth manifold. These singularity types are not identical and can neither be distinguished nor identified by simply investigating the rank deficiency of the constraint Jacobian (linear dependence of joint screws). C-space singularities are reflected by the c-space geometry. In a previous work, a kinematic tangent cone was introduced as an approximation of the c-space, defined as the set of tangents to smooth curves in c-space. Identification of kinematic singularities amounts to analyze the local geometry of the set of critical points. As a computational means, a kinematic tangent cone to the set of critical points is introduced in terms of Jacobian minors. Closed form expressions for the derivatives of the minors in terms of Lie brackets of joint screws are presented. A computational method is introduced to determine a polynomial system defining the kinematic tangent cone. The paper complements the recently proposed mobility analysis using the tangent cone to the c-space. This allows for identifying c-space and kinematic singularities as long as the solution set of the constraints is a real variety. The introduced approach is directly applicable to the higher-order analysis of forward kinematic singularities of serial manipulators. This is briefly addressed in the paper.

Forward kinematic singularity avoiding design of a Schönflies motion generator by asymmetric attachment of subchains

In most of the previous studies on parallel mechanisms (PMs), architectural design mainly relying on symmetric geometry was investigated without in-depth analysis of its performance. This work demonstrates that such a symmetric geometry of multiple subchains sometimes induces a forward kinematic singularity which degrades the overall kinematic performance of PMs within the desired workspace and claims that an asymmetric attachment of those subchains on a moving platform can effectively resolve such a singularity problem. A 4-Degree-of-Freedom (DOF) PM exhibiting Schonflies motions is examined as an example device. First, its mobility analysis and kinematic modeling via screw theory are conducted. Then a singularity analysis based on Grassmann line geometric conditions is carried out, and the forward kinematic singularities of the mechanism are identified and verified by simulations. Based on these analysis and simulations, a forward kinematic singularity-free design is suggested. To show the high potential of the device in practical applications, its output stiffness and dynamic motion capability are examined. Then a prototype is built and its motions capability is verified through experiments.