A simple method to solve the forward displacement analysis of the general six-legged parallel manipulator

In this work a simple method to solve the forward displacement analysis of the general 6-6 fully parallel manipulator is applied. The method is based on generating closure equations upon the unknown coordinates of three points embedded to the moving platform. The method is easy to follow and it is available for both, planar and three-dimensional moving platforms. Numerical examples are included with the purpose to show the application of the method.     

Jerk analysis of a six-degrees-of-freedom three-legged parallel manipulator

In this work the jerk analysis of a 3-RRPS parallel manipulator to realize six degrees of freedom is approached by means of the theory of screws. The input/output equations of velocity, acceleration and jerk of the moving platform with respect to the fixed platform are obtained systematically by resorting to reciprocal-screw theory. A numerical example is included in order to show the application of the method of kinematic analysis. Furthermore, the numerical results obtained via screw theory are satisfactorily compared with simulations generated with the aid of commercially available software.     

A simple approach to solving the kinematics of the 4-UPS/PS (3R1T) parallel manipulator

Journal of Mechanical Science and Technology - This work reports on the position, velocity and acceleration analyses of a four-degrees-of-freedom parallel manipulator, 4-DoF-PM for brevity, which...     

Kinematics of a Hybrid Manipulator by Means of Screw Theory

In this work the kinematics of a hybrid manipulator, namely a fully parallel-serial manipulator, with a particular topology is approached by means of the theory of screws. Given the length of the six independent limbs, the forward position analysis of the mechanism under study, indeed the computation of the resulting pose, position and orientation, of the end-platform with respect to the fixed platform, is carried out in closed-form solution. Therefore conveniently this initial analysis avoids the use of a numerical technique such as the Newton-Raphson method. Writing in screw form the reduced acceleration state of the translational platform, with respect to the fixed platform, a simple expression for the computation of the acceleration of the translational platform is derived by taking advantage of the properties of reciprocal screws, via the Klein form, a bilinear symmetric form of the Lie algebra e(3). Following a similar procedure, a simple expression for the computation of the angular acceleration of the end-platform, with respect to the translational platform, is easily derived. Naturally, as an intermediate step, this contribution also provides the forward and inverse velocity analyses of the chosen parallel-serial manipulator. Finally, in order to prove the versatility of the expressions obtained via screw theory for solving the kinematics, up to the acceleration analysis, of the proposed spatial mechanism, a numerical example is solved with the help of commercial computer codes.     

An application of screw theory to the kinematic analysis of a Delta-type robot

This paper reports on the kinematics of a translational parallel manipulator whose topology is close to the architecture of the famous Delta robot. The displacement analysis is presented in closed-form solution by applying a new strategy based on the unknown coordinates of a point embedded to the moving platform. The input-output equations of velocity and acceleration of the robot are systematically obtained by resorting to reciprocal-screw theory. The singularities of the mechanism are explained through the input-output equation of velocity. Finally, a numerical example is provided to show the application of the method.     

Hyper-Jerk Analysis of Robot Manipulators

In this work the hyper-jerk analysis of robot manipulators is addressed by means of the theory of screws. The reduced hyper-jerk state of a rigid body as observed from another body or reference frame is obtained as a six-dimensional vector by applying the concept of helicoidal vector field. Moreover, this contribution demonstrates that the reduced hyper-jerk state of a rigid body can be considered, similar to the velocity state, as a twist about a screw. Furthermore, the reduced hyper-jerk state is systematically obtained in pure screw form. Finally, a case study, which is verified with the aid of commercially available software, that consists of solving the kinematics, up to the hyper-jerk analysis, of a zero-torsion parallel manipulator is included in order to show the application of the method of kinematic analysis.     

Mobility analysis and kinematics of the semi-general 2(3-RPS) series-parallel manipulator

This work reports on the kinematics of a series-parallel manipulator built with two zero-torsion tangential parallel manipulators assembled in series connection. Although this mechanism has been widely studied, there are some topics that must be revised, e.g. the mobility analysis here reported shows that the robot under study is not precisely a six degrees of freedom spatial mechanism as it has been commonly considered. Furthermore, the traditional hexagonal coupler platform is replaced with a three-dimensional platform which yields a mechanism with a more general topology. The forward and inverse displacement analyses of the robot are obtained in semi-closed form solutions based on simple closure equations which are generated upon the coordinates of three points embedded to the moving platform while the input–output equations of velocity and acceleration of the semi-general series-parallel manipulator are easily derived by resorting to reciprocal-screw theory. A case study is included in order to show the application of the method of kinematic analysis.     

Inverse jerk analysis of symmetric zero-torsion parallel manipulators

In this work the inverse velocity, acceleration and jerk analyses of a class of three-degrees-of-freedom parallel manipulators are approached by means of the theory of screws. The concept of reciprocal screws allows to obtain simple and decoupled expressions to compute the joint rates, up to the third time derivative, of the class of manipulators under study given the instantaneous kinematic properties of the center of the moving platform. The interdependency between the angular and linear kinematic properties of the moving platform is also derived. A case study is included.     

Solving the kinematics and dynamics of a modular spatial hyper-redundant manipulator by means of screw theory

In this contribution, a systematic methodology for solving the kinematic and dynamic analyses of a modular spatial hyper-redundant manipulator built with an optional number of serially connected three-legged in-parallel manipulators are presented. First, the kinematics and dynamics of the base module are carried out using the theory of screws and the principle of virtual work. Next, the expressions obtained for the base module are extended without significant effort to the spatial hyper-redundant manipulator under study. Finally, the proposed methodology of analysis is applied to a 18 degrees of freedom hyper-redundant manipulator.