Manuscript received March 8, ; final manuscript received March 2, ; published online August 23, Editor: Eugenio Schuster. Huang, J. August 23, November ; 6 : A novel Udwadia-Kalaba approach for parallel manipulator dynamics analysis is presented.

## Kinematics of a Hybrid Manipulator by Means of Screw Theory

The approach segments a parallel manipulator system into several leg-subsystems and the platform subsystem, which are connected by kinematic constraints. The Udwadia-Kalaba equation is then used to calculate the constraint forces due to the constraints. Based on this, the equation of motion, which is an explicit i. The method allows a systematic procedure to generate the dynamic model for both direct dynamics and inverse dynamics without invoking additional variables such as multipliers or quasi-variablesnor does it require projection.

A classical parallel Stewart-Gough platform is chosen to demonstrate the feasibility and advantages of this approach. Sign In or Create an Account. Sign In. Advanced Search. Article Navigation. Close mobile search navigation Article navigation.

VolumeIssue 6. Previous Article Next Article. The State Key Laboratory of Advanced. This Site. Google Scholar. ChenY. Chen 2. Professor The George W. Woodruff School. Zhihua Zhong Zhihua Zhong. Author and Article Information. Jin Huang. Nov6 : 11 pages. Published Online: August 23, Article history Received:. Revision Received:. Views Icon Views. Cite Icon Cite. Issue Section:.DOI : Background: The vector propulsion device can significantly improve the sensitivity and mobility of the mechanism.

Furthermore, thrust vectoring technology with single manipulator and multidimensional attitude is a novel thrust vectoring technique in industry, especially in aviation fields. Numerous progresses made by various research groups and the newest patents in these aspects will be cited in this paper. Methods: Firstly, in the framework of screw theory, the topological structure of the spherical parallel mechanism was modeled to analyze the motion characteristics. Secondly, in terms of closed chain constraint equations, the vectored algebra method was employed to derive the Jacobian matrix of the mechanism.

Thirdly, the decoupling structure configuration method was adopted to establish the analytical model of velocity and acceleration. Finally, the dynamic model was established by means of virtual work principle. Results: The forward and inverse solutions of the mechanism was calculated; the Jacobian matrix of the mechanism was derived; the kinematic characters including singularity and dexterity were analyzed; the performance analysis was carried out.

Conclusion: This new type of underwater vehicle oriented power plant, which is characterized by simple decoupling structure, strong steering capability, and high cost-efficiency, has broad prospects in the field of AUV. Keywords: Autonomous underwater vehicles, dynamic model, performance, screw theory, spherical parallel mechanism, vectored thruster.

Abstract: Background: The vector propulsion device can significantly improve the sensitivity and mobility of the mechanism. Furthermore, thrust vectoring technol Volume 13Issue 1 Journal Home.

A study on simultaneous design of a Hall Effect Thruster and its low-thrust trajectory. Acta Astronautica ; Experiences and results from designing and developing a 6 DOF underwater parallel robot. Robot Auton Syst ; Nonlinear mathematics modeling and analysis of the vectored thruster autonomous underwater vehicle in 6-DOF motions.

J Mech Eng ; 47 5 : Rotor assembly having thrust vectoring capabilities. US Screw theory is the algebraic calculation of pairs of vectors, such as forces and moments or angular and linear velocity, that arise in the kinematics and dynamics of rigid bodies. Screw theory provides a mathematical formulation for the geometry of lines which is central to rigid body dynamicswhere lines form the screw axes of spatial movement and the lines of action of forces.

An important result of screw theory is that geometric calculations for points using vectors have parallel geometric calculations for lines obtained by replacing vectors with screws. This is termed the transfer principle. Screw theory has become an important tool in robot mechanics, [5] [6] mechanical design, computational geometry and multibody dynamics.

This is in part because of the relationship between screws and dual quaternions which have been used to interpolate rigid-body motions. Felix Klein saw screw theory as an application of elliptic geometry and his Erlangen Program. The use of a symmetric matrix for a von Staudt conic and metric, applied to screws, has been described by Harvey Lipkin. CliffordF. DimentbergKenneth H. HuntJ. A spatial displacement of a rigid body can be defined by a rotation about a line and a translation along the same line, called a screw displacement.

This is known as Chasles' theorem. For comparison, the six parameters that define a spatial displacement can also be given by three Euler Angles that define the rotation and the three components of the translation vector. A screw is a six-dimensional vector constructed from a pair of three-dimensional vectors, such as forces and torques and linear and angular velocity, that arise in the study of spatial rigid body movement.

The force and torque vectors that arise in applying Newton's laws to a rigid body can be assembled into a screw called a wrench. A torque, on the other hand, is a pure moment that is not bound to a line in space and is an infinite pitch screw. The ratio of these two magnitudes defines the pitch of the screw.

A twist represents the velocity of a rigid body as an angular velocity around an axis and a linear velocity along this axis.

All points in the body have the same component of the velocity along the axis, however the greater the distance from the axis the greater the velocity in the plane perpendicular to this axis. Thus, the helicoidal field formed by the velocity vectors in a moving rigid body flattens out the further the points are radially from the twist axis.

The points in a body undergoing a constant screw motion trace helices in the fixed frame.

### Dynamic Modelling of Lower Mobility Parallel Manipulators

If this screw motion has zero pitch then the trajectories trace circles, and the movement is a pure rotation.December 23, May ; 72 3 : Various modeling approaches proposed in the literature build upon the classical formulations for serial manipulators, and thus, inherit those modeling conventions that tend to be restrictive rather than user-friendly. Moreover, the special kinematic topology of PKM is treated either ad hoc or by resolving loop constraints using standard methods from multibody dynamics.

Geometric formulations on the other hand, more precisely Lie group formulations, were developed over the last decades that provide a flexible and user-friendly approach to the modeling of robotic systems in general. A dedicated formulation for topologically simple PKM has not yet been proposed, however. Such a formulation is presented in this paper.

The frame invariance of the geometric formulation gives rise to a modular modeling approach that further reduces the modeling effort.

The equations of motion EOM in terms of task space coordinates as well as in actuator coordinates are presented for kinematically nonredundant and redundant topologically simple PKMs. A PKM is topologically simple if its moving platform is connected to the base by simple serial kinematic chains and if there are no other kinematic chains than these.

Applications of the EOM for dynamics simulation and model-based control are briefly discussed. The paper also provides a literature review of approaches to dynamics modeling of PKM. Sign In or Create an Account. Sign In. Advanced Search. Article Navigation. Close mobile search navigation Article navigation. Volume 72, Issue 3.

## Kinematics of a Hybrid Manipulator by Means of Screw Theory

Next Article. Review Articles. Insitute of Robotics, Johannes Kepler University. This Site. Google Scholar. Author and Article Information. May72 3 : 27 pages. Published Online: December 23, 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. This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. Tol, U. Bonev, I. Agrawal, S. Gosselin, C.

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**Modern Robotics, Chapter 7: Kinematics of Closed Chains**

Merlet, J. Mohamed, M. Parenti-Castelli, V. Tsai, L. Wang, J. Raghavan, M. Rico, J. Romdhane, L. Ball, R. Fang, Y. Bayro-Corrochano, E. Baker and K. Wohlhart eds. Roth, B. Brady and R.Sign up now and have it sent straight to your inbox. Daily and Weekly newsletters available.

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## Dynamics of parallel manipulators by means of screw theory