Recursive Kinematics and Inverse Dynamics for Parallel Manipulators

2003 ◽  
Author(s):  
Waseem A. Khan ◽  
Venkat N. Krovi ◽  
Subir K. Saha ◽  
Jorge Angeles
Keyword(s):  
Inverse Dynamics ◽  
Parallel Architecture ◽  
Parallel Manipulators ◽  
Orthogonal Complement ◽  
Recursive Formulation

We examine here the modular and recursive formulation of the inverse dynamics of parallel architecture mainpulators. The concept of the decoupled natural orthogonal complement (DeNOC) is combined with the spatial parallelism of the robots of interest to develop an inverse dynamics algorithm which is both recursive and modular.

Recursive Kinematics and Inverse Dynamics for a Planar 3R Parallel Manipulator

2004 ◽  
Vol 127 (4) ◽  
pp. 529-536 ◽  
Author(s):  
Waseem A. Khan ◽  
Venkat N. Krovi ◽  
Subir K. Saha ◽  
Jorge Angeles
Keyword(s):  
Mathematical Models ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Parallel Architecture ◽  
Robotic Systems ◽  
Orthogonal Complement ◽  
Recursive Algorithms ◽  
Planar Parallel Manipulator ◽  
Kinematic Loops

We focus on the development of modular and recursive formulations for the inverse dynamics of parallel architecture manipulators in this paper. The modular formulation of mathematical models is attractive especially when existing sub-models may be assembled to create different topologies, e.g., cooperative robotic systems. Recursive algorithms are desirable from the viewpoint of simplicity and uniformity of computation. However, the prominent features of parallel architecture manipulators-the multiple closed kinematic loops, varying locations of actuation together with mixtures of active and passive joints-have traditionally hindered the formulation of modular and recursive algorithms. In this paper, the concept of the decoupled natural orthogonal complement (DeNOC) is combined with the spatial parallelism of the robots of interest to develop an inverse dynamics algorithm which is both recursive and modular. The various formulation stages in this process are highlighted using the illustrative example of a 3R Planar Parallel Manipulator.

Singularity robust inverse dynamics of planar 2-RPR parallel manipulators

2004 ◽  
Vol 218 (7) ◽  
pp. 721-730 ◽  
Author(s):  
S Kemal Ider
Keyword(s):  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Full Rank ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Dynamic Equations ◽  
Revolute Joints ◽  
Planar Parallel Manipulator ◽  
Pass Through ◽  
Full Utilization

In planar parallel robots, limitations occur in the functional workspace because of interference of the legs with each other and because of drive singularities where the actuators lose control of the moving platform and the actuator forces grow without bounds. A 2-RPR (revolute, prismatic, revolute joints) planar parallel manipulator with two legs that minimizes the interference of the mechanical components is considered. Avoidance of the drive singularities is in general not desirable since it reduces the functional workspace. An inverse dynamics algorithm with singularity robustness is formulated allowing full utilization of the workspace. It is shown that if the trajectory is planned to satisfy certain conditions related to the consistency of the dynamic equations, the manipulator can pass through the drive singularities while the actuator forces remain stable. Furthermore, for finding the actuator forces in the vicinity of the singular positions a full rank modification of the dynamic equations is developed. A deployment motion is analysed to illustrate the proposed approach.

Inverse Dynamics Algorithm for Space Robots

1996 ◽  
Vol 118 (3) ◽  
pp. 625-629 ◽  
Author(s):  
Subir Kumar Saha
Keyword(s):  
Efficient Algorithm ◽  
Dynamic Models ◽  
Inverse Dynamics ◽  
Recursive Algorithm ◽  
Space Robot ◽  
Orthogonal Complement ◽  
Free Base ◽  
Space Robots ◽  
Primary Body ◽  
Kinematic Models

An efficient algorithm for the inverse dynamics of free-flying space robots, consisting of a serial manipulator mounted on a free-base, e.g., a spacecraft, is presented. The kinematic and dynamic models are based on the concepts of the Primary Body (PB) and the Natural Orthogonal Complement, respectively, reported elsewhere. In this paper, besides the efficiency, the usefulness of the PB in deriving different kinematic models and selecting an efficient one is pointed out. Moreover, it is shown that a recursive algorithm for the inverse dynamics of the space robot at hand can be developed even without the consideration of the momenta conservation principle.

Path Tracking of Parallel Manipulators in the Presence of Force Singularity

2005 ◽  
Vol 127 (4) ◽  
pp. 550-563 ◽  
Author(s):  
C. K. Kevin Jui ◽  
Qiao Sun
Keyword(s):  
Motion Planning ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Parallel Manipulators ◽  
Path Tracking ◽  
Singularity Avoidance ◽  
Design Complexity ◽  
Actuation Redundancy ◽  
Planar Parallel Manipulator ◽  
Simulation Results

Parallel manipulators are uncontrollable at force singularities due to the infeasibly high actuator forces required. Existing remedies include the application of actuation redundancy and motion planning for singularity avoidance. While actuation redundancy increases cost and design complexity, singularity avoidance reduces the effective workspace of a parallel manipulator. This article presents a path tracking type of approach to operate parallel manipulators when passing through force singularities. We study motion feasibility in the neighborhood of singularity and conclude that a parallel manipulator may track a path through singular poses if its velocity and acceleration are properly constrained. Techniques for path verification and tracking are presented, and an inverse dynamics algorithm that takes actuator bounds into account is examined. Simulation results for a planar parallel manipulator are given to demonstrate the details of this approach.

Analysis of Varying Natural Frequencies and Damping Ratios of a Sample Parallel Manipulator Throughout its Workspace Using Linearized Equations of Motion

2001 ◽  
Author(s):  
Kris Kozak ◽  
Imme Ebert-Uphoff ◽  
William Singhose
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Parallel Architecture ◽  
Robotic Manipulators ◽  
Parallel Manipulators ◽  
Dynamic Equations ◽  
Extreme Variation

Abstract This article investigates the dynamic properties of robotic manipulators of parallel architecture. In particular, the dependency of the dynamic equations on the manipulator’s configuration within the workspace is analyzed. The proposed approach is to linearize the dynamic equations locally throughout the workspace and to plot the corresponding natural frequencies and damping ratios. While the results are only applicable for small velocities of the manipulator, they present a first step towards the classification of the nonlinear dynamics of parallel manipulators. The method is applied to a sample manipulator with two degrees-of-freedom. The corresponding numerical results demonstrate the extreme variation of its natural frequencies and damping ratios throughout the workspace.

An efficient method for the dynamic modeling and analysis of Stewart parallel manipulator based on the screw theory

2019 ◽  
Vol 234 (3) ◽  
pp. 808-821
Author(s):  
Yulei Hou ◽  
Guoxing Zhang ◽  
Daxing Zeng
Keyword(s):  
Dynamic Model ◽  
Dynamic Modeling ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Force Balance ◽  
Constraint Matrix ◽  
Scheme Design ◽  
Control Scheme

Dynamic modeling serves as the fundamental basis for dynamic performance analysis and is an essential aspect of the control scheme design of parallel manipulators. This report presents a concise and efficient solution to the dynamics of Stewart parallel manipulators based on the screw theory. The initial pose of these manipulators is described. Then the pose matrix of each link of the Stewart parallel mechanism is obtained using an inverse kinematics solution and an exponential product formula. Considering the constraint relationship between joints, the constraint matrix of the Stewart parallel manipulator is deduced. In addition, the Jacobian matrix and the twist of each link are obtained. Moreover, by deriving the differential form of the constraint matrix, the spatial acceleration of each link is obtained. Based on the force balance relationship of each link, the inverse dynamics and the general form of the dynamic model of the Stewart parallel manipulator is established and the process of inverse dynamics is summarized. The dynamic model is then verified via dynamic simulation using the ADAMS software. A numerical example is considered to demonstrate the feasibility and effectiveness of this model. The proposed dynamic modeling approach serves as a fundamental basis for structural optimization and control scheme design of the Stewart parallel manipulators.

Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices

1999 ◽  
Vol 66 (4) ◽  
pp. 986-996 ◽  
Author(s):  
S. K. Saha
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Kinematic Chain ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Orthogonal Complement ◽  
Forward Dynamics ◽  
Velocity Constraints

Constrained dynamic equations of motion of serial multibody systems consisting of rigid bodies in a serial kinematic chain are derived in this paper. First, the Newton-Euler equations of motion of the decoupled rigid bodies of the system at hand are written. Then, with the aid of the decoupled natural orthogonal complement (DeNOC) matrices associated with the velocity constraints of the connecting bodies, the Euler-Lagrange independent equations of motion are derived. The De NOC is essentially the decoupled form of the natural orthogonal complement (NOC) matrix, introduced elsewhere. Whereas the use of the latter provides recursive order n—n being the degrees-of-freedom of the system at hand—inverse dynamics and order n3 forward dynamics algorithms, respectively, the former leads to recursive order n algorithms for both the cases. The order n algorithms are desirable not only for their computational efficiency but also for their numerical stability, particularly, in forward dynamics and simulation, where the system’s accelerations are solved from the dynamic equations of motion and subsequently integrated numerically. The algorithms are illustrated with a three-link three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm.

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