Instantaneous Kinematics of Parallel-Chain Robotic Mechanisms

1992 ◽  
Vol 114 (3) ◽  
pp. 349-358 ◽  
Author(s):  
V. Kumar
Keyword(s):  
Inverse Kinematics ◽  
Robotic Manipulators ◽  
Parallel Manipulators ◽  
Parallel Structure ◽  
End Effector ◽  
Serial Manipulators ◽  
Parallel Scheme ◽  
Parallel Chain ◽  
Manipulation System ◽  
Dual Arm

This paper addresses the instantaneous kinematics of robotic manipulators which have an in-parallel scheme of actuation. Hybrid geometries which require both serial and parallel actuation are also considered. Multifingered grippers, walking vehicles, and multiarm manipulation systems in addition to robot arms with a parallel structure can be included in this broad category. The direct and inverse kinematics (and statics) of these devices is discussed with particular attention to applications in control. An analytical method based on screw system theory for obtaining transformation equations between joint and end-effector coordinates is described. Special configurations in which the end-effector gains or loses a degree of freedom, which are also known as geometric singularities, are an important consideration in this study. This is because the number of special configurations or singularities in the workspace is far more for in-parallel manipulators than that for serial manipulators. The special configurations for a planar dual-arm manipulation system, which can be kinematically modeled as a 5-R linkage, are discussed in some detail as an example.

Inverse Kinematics of Discretely-Actuated Manipulators Within a Bounded Grid Element

2006 ◽  
Author(s):  
Deanne C. Kemeny ◽  
Raymond J. Cipra
Keyword(s):  
Inverse Kinematics ◽  
Lower Cost ◽  
Robotic Manipulators ◽  
Forward Kinematics ◽  
End Effector ◽  
Grid Element ◽  
The Third ◽  
Inverse Kinematics Problem

Discretely-actuated manipulators are defined in this paper as serial planar chains of many links and are an alternative to traditional robotic manipulators, where continuously variable actuators are replaced with discrete, or digital actuators. Benefits include reduced weight and complexity, and predictable manipulation at lower cost. Challenges to using digital manipulators are the discrete end-effector positions which make the inverse kinematics problem difficult to solve. Furthermore, for a specific application position in the manipulator workspace, there may not be an actual end-effector position. This research has relaxed the inverse kinematics problem around this challenge making each application position an element of a grid in which the end effector must reach. There may be many possible end-effector positions that would reach the element goal, the solution uses the first one that is found. The inverse kinematics solution assumes the assembly configuration of the digital manipulator is already solved specifically for the application grid. The Jacobian function, normally used to solve joint velocities, can be used to identify the exact shift vectors that are used for the inverse kinematics. Three methods to solve this problem are discussed and the third method was implemented as a four-part solution that is a directed and manipulated search for the inverse kinematics solution where all four solutions may be needed. A discussion of forward kinematics and the Jacobian function in relation to digital manipulators is also presented.

On the Numerical Inverse Kinematics of Robotic Manipulators

1987 ◽  
Vol 109 (1) ◽  
pp. 8-13 ◽  
Author(s):  
Kazem Kazerounian
Keyword(s):  
Inverse Kinematics ◽  
Robotic Manipulators ◽  
Analysis Method ◽  
Computationally Efficient ◽  
Serial Manipulators ◽  
Position Analysis ◽  
Zero Position

Based on the sequential motion of joints, a method is developed for the numerical inverse kinematics of serial manipulators. This algorithm is stable and computationally efficient and uses the zero position analysis method for robotic manipulators.

A Class of Parallel Manipulators Based on Kinematically Simple Branches

1994 ◽  
Vol 116 (3) ◽  
pp. 908-914 ◽  
Author(s):  
R. P. Podhorodeski ◽  
K. H. Pittens
Keyword(s):  
Parallel Manipulators ◽  
Parallel Structure ◽  
End Effector ◽  
Forward Displacement ◽  
Parallel Class ◽  
Serial Chain ◽  
Order Polynomial ◽  
Six Dof ◽  
Actuated Joints ◽  
Chain Branch

Parallel manipulators consisting of serial branches acting in parallel on a common end effector are examined. All nonredundant, six DOF manipulators corresponding to this in-parallel class of structures are enumerated. A specific in-parallel structure, three branches with two actuated joints per branch (3–2,2,2), is chosen as most promising based upon performance considerations. A class of kimematically simple (KS) serial-chain branch joint layouts suitable for the chosen in-parallel structure is defined. Arguments based upon kinematic equivalency of the branches and mobility of the assembled in-parallel manipulator chain are used to show that there exist only five unique branch joint-layouts belonging to the KS class. It is demonstrated that the solution to the inverse displacement problem for in-parallel manipulators based on the KS branches can be expressed in a closed form. Furthermore, the 3–2,2,2 in-parallel manipulators are shown to belong to a family of manipulators whose forward displacement solutions can be resolved through roots of a 16th order polynomial.

DeltaBot: A New Cable-Based Ultra High Speed Robot

2003 ◽  
Author(s):  
Saeed Behzadipour ◽  
Robert Dekker ◽  
Amir Khajepour ◽  
Edmon Chan
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Manufacturing Industry ◽  
Design Procedure ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Parallel Robots ◽  
Manufacturing Cost ◽  
End Effector ◽  
Serial Manipulators

The growing needs for high speed positioning devices in the automated manufacturing industry have been challenged by robotic science for more than two decades. Parallel manipulators have been widely used for this purpose due to their advantage of lower moving inertia over the conventional serial manipulators. Cable actuated parallel robots were introduced in 1980’s to reduce the moving inertia even further. In this work, a new cable-based parallel robot is introduced. For this robot, the cables are used not only to actuate the end-effector but also to apply the necessary kinematic constraints to provide three pure translational degrees of freedom. In order to maintain tension in the cables, a passive air cylinder is used to push the end-effector against the stationary platform. In addition to low moving inertia, the new design benefits from simplicity and low manufacturing cost by eliminating joints from the robot’s mechanism. The design procedure and the results of experiments will be discussed in the following.

Inverse Kinematics for Planar Parallel Manipulators

1997 ◽  
Author(s):  
Robert L. Williams ◽  
Brett H. Shelley
Keyword(s):  
Inverse Kinematics ◽  
Broad Class ◽  
Parallel Manipulators ◽  
End Effector ◽  
Serial Chain ◽  
Prismatic Joints ◽  
Inverse Solutions ◽  
Three Degree Of Freedom ◽  
Serial Chains ◽  
Planar Parallel Manipulators

Abstract This paper presents algebraic inverse position and velocity kinematics solutions for a broad class of three degree-of-freedom planar in-parallel-actuated manipulators. Given an end-effector pose and rate, all active and passive joint values and rates are calculated independently for each serial chain connecting the ground link to the end-effector link. The solutions are independent of joint actuation. Seven serial chains consisting of revolute and prismatic joints are identified and their inverse solutions presented. To reduce computations, inverse Jacobian matrices for overall manipulators are derived to give only actuated joint rates. This matrix yields conditions for invalid actuation schemes. Simulation examples are given.

Kinematic and Kinetostatic Analysis of Parallel Manipulators with Emphasis on Position, Motion, and Actuation Singularities

Robotica ◽  
2018 ◽  
Vol 37 (4) ◽  
pp. 599-625 ◽  
Author(s):  
M. Kemal Ozgoren
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
The Other ◽  
Forward Kinematics ◽  
Velocity Mapping ◽  
Active Joint ◽  
End Effector ◽  
Jacobian Matrices ◽  
Other Hand

SummaryThis paper provides a contribution to the singularity analysis of the parallel manipulators by introducing the position singularities in addition to the motion and actuation singularities. The motion singularities are associated with the linear velocity mapping between the task and joint spaces. So, they are the singularities of the relevant Jacobian matrices. On the other hand, the position singularities are associated with the nonlinear position mapping between the task and joint spaces. So, they are encountered in the position-level solutions of the forward and inverse kinematics problems. In other words, they come out irrespective of the velocity mapping and the Jacobian matrices. Considering these distinctions, a kinematic singularity is denoted here by one of the four acronyms, which are PSFK (position singularity of forward kinematics), PSIK (position singularity of inverse kinematics), MSFK (motion singularity of forward kinematics), and MSIK (motion singularity of inverse kinematics). There may also occur an actuation singularity (ACTS) concerning the kinetostatic relationships that involve forces and moments. However, it is verified that an ACTS is the same as an MSFK. Each singularity induces different consequences in the joint and task spaces. A PSFK imposes a constraint on the active joint variables and makes the end-effector position indefinite and uncontrollable. Therefore, it must be avoided. An MSFK imposes a constraint on the rates of the active joint variables and makes the end-effector motion indefinite and easily perturbable. Besides, since it is also an ACTS, it causes the actuator torques or forces to grow without bound. Therefore, it must also be avoided. On the other hand, a PSIK imposes a constraint on the end-effector position but provides freedom for the active joint variables. Similarly, an MSIK imposes a constraint on the end-effector motion but provides freedom for the rates of the active joint variables. A PSIK or MSIK need not be avoided if the constraint it imposes on the position or motion of the end-effector is acceptable or if the task can be planned to be compatible with that constraint. Besides, with such a compatible task, a PSIK or MSIK may even be advantageous, because the freedom it provides for the active joint variables can sometimes be used for a secondary purpose. This paper is also concerned with the multiplicities of forward kinematics in the assembly modes of the manipulator and the multiplicities of inverse kinematics in the posture modes of the legs. It is shown that the assembly mode changing poses of the manipulator are the same as the MSFK poses, and the posture mode changing poses of the legs are the same as the MSIK poses.

scholarly journals Position and Singularity Analysis of a Class of Planar Parallel Manipulators with a Reconfigurable End-Effector

Machines ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 7
Author(s):  
Tommaso Marchi ◽  
Giovanni Mottola ◽  
Josep M. Porta ◽  
Federico Thomas ◽  
Marco Carricato
Keyword(s):  
Inverse Kinematics ◽  
Kinematic Chain ◽  
Experimental Tests ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Parallel Robots ◽  
End Effector ◽  
Revolute Joints ◽  
A Chain ◽  
And Control

Parallel robots with configurable platforms are a class of robots in which the end-effector has an inner mobility, so that its overall shape can be reconfigured: in most cases, the end-effector is thus a closed-loop kinematic chain composed of rigid links. These robots have a greater flexibility in their motion and control with respect to rigid-platform parallel architectures, but their kinematics is more challenging to analyze. In our work, we consider n-RRR planar configurable robots, in which the end-effector is a chain composed of n links and revolute joints, and is controlled by n rotary actuators located on the base of the mechanism. In particular, we study the geometrical design of such robots and their direct and inverse kinematics for n=4, n=5 and n=6; we employ the bilateration method, which can simplify the kinematic analysis and allows us to generalize the approach and the results obtained for the 3-RRR mechanism to n-RRR robots (with n>3). Then, we study the singularity configurations of these robot architectures. Finally, we present the results from experimental tests that have been performed on a 5–RRR robot prototype.

scholarly journals Investigating Task Prioritization and Holistic Coordination Using Relative Jacobian for Combined 3-Arm Cooperating Parallel Manipulators

2016 ◽  
Vol 20 (1) ◽  
pp. 117-123 ◽  
Author(s):  
Rodrigo S. Jamisola Jr. ◽  
◽  
Frank Ayo Ibikunle
Keyword(s):  
Null Space ◽  
Holistic Approach ◽  
Parallel Manipulators ◽  
Previous Method ◽  
End Effector ◽  
Task Prioritization ◽  
New Formulation ◽  
Prioritization Scheme ◽  
Dual Arm ◽  
Manipulator Control

A new modular relative Jacobian formulation for single end-effector control of combined 3-arm cooperating parallel manipulators is derived. It is based on a previous method of derivation for dual-arm robots, with the same approach of modularity and single end-effector control for combined manipulators. This paper will present this new formulation, as well as investigate task prioritization scheme to verify the claim that a single end-effector controller of combined manipulators will indeed implement a strict task prioritization, by intentionally adding more tasks. In addition, this paper will investigate a claim that the holistic approach to control of combined manipulators affords easier control coordination of each of the stand-alone components. Switching control from an individual manipulator control in the null space to relative control in the tasks space is shown to investigate the smoothness of task execution during switching. Simulation results using Gazebo 2.2.5 running in Ubuntu 14.04 is shown.

scholarly journals Passive Compliance Control of Redundant Serial Manipulators

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
Jacob J. Rice ◽  
Joseph M. Schimmels
Keyword(s):  
Inverse Kinematics ◽  
Joint Stiffness ◽  
Contact Forces ◽  
Elastic Behavior ◽  
Time Varying ◽  
Compliance Control ◽  
End Effector ◽  
Serial Manipulators ◽  
Passive Compliance ◽  
External Loads

Passive compliance control is an approach for controlling the contact forces between a robotic manipulator and a stiff environment. This paper considers passive compliance control using redundant serial manipulators with real-time adjustable joint stiffness. Such manipulators can control the elastic behavior of the end-effector by adjusting the manipulator configuration and by adjusting the intrinsic joint stiffness. The end-effector's time-varying elastic behavior is a beneficial quality for constrained manipulation tasks such as opening doors, turning cranks, and assembling parts. The challenge in passive compliance control is finding suitable joint commands for producing the desired time-varying end-effector position and compliance (task manipulation plan). This problem is addressed by extending the redundant inverse kinematics (RIK) problem to include compliance. This paper presents an effective method for simultaneously attaining the desired end-effector position and end-effector elastic behavior by tracking a desired variation in both the position and the compliance. The set of suitable joint commands is not unique; the method resolves the redundancy by minimizing the actuator velocity norm. The method also compensates for joint deflection due to known external loads, e.g., gravity.

The kinematics and statics of manipulators

2009 ◽  
Vol 223 (9) ◽  
pp. 2155-2166 ◽  
Author(s):  
J-S Zhao ◽  
W Lu ◽  
F Chu ◽  
Z-J Feng
Keyword(s):  
Path Planning ◽  
Inverse Kinematics ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Static Balance ◽  
Kinematics Analysis ◽  
Virtual Power ◽  
End Effector ◽  
Forward And Inverse Kinematics ◽  
Inverse Velocity

As the kinematics and statics play a very important role in determining the actuating inputs and the effective loads that the end-effector sustains, this article focuses on this issue and proposes an analytical process to study the forward and inverse kinematics and statics of spatial manipulators. As series manipulators and parallel manipulators show different features in kinematics and statics, this article discusses them separately. First, the forward and inverse velocity problems of the manipulator linkages are investigated with reciprocal screw theory. Then, the static balance conditions together with forward and inverse statics of the manipulator linkages are established through virtual power theory. In the kinematics analysis, the primary conditions for feasible motions of an end-effector are addressed through velocity screws. Illustrative examples indicate that the method proposed in this article can be used to guide the singularity identification, path planning, and feasible motion determination.

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