Parameterization of Three-Dimensional Rigid Body Guidance Incorporating Planar Gear Connections in a Spatial Closed-Loop Mechanism With Parallel Consecutive Axes

This paper introduces a reconfigurable closed-loop spatial mechanism that can be applied to repetitive motion tasks. The concept is to incorporate five pairs of non-circular gears into a six degree-of–freedom closed-loop spatial chain. The gear pairs are designed based on given mechanism parameters and a user defined motion specification of a coupler link of the mechanism. It is shown in the paper that planar gear pairs can be used if the spatial closed-loop chain is comprised of six pairs of parallel joint axes, i.e. the first joint axis is parallel to the second, the third is parallel to the fourth, ..., and the eleventh is parallel to the twelfth. This paper presents the synthesis of the gear pairs that satisfy a specified three-dimensional position and orientation need. Numerical approximations were used in the synthesis the non-circular gear pairs by introducing an auxiliary monotonic parameter associated to each end-effector position to parameterize the motion needs. The findings are supported by a computer animation. No previous known literature incorporates planar non-circular gears to fulfill spatial motion generation needs.

Reverse Kinematic Analysis of the Spatial Six Axis Robotic Manipulator With Consecutive Joint Axes Parallel

Volume 8: 31st Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2007-34433 ◽

2007 ◽

Cited By ~ 1

Author(s):

Javier Rolda´n Mckinley ◽

Carl Crane ◽

David B. Dooner

Keyword(s):

Kinematic Analysis ◽

Closed Loop ◽

Degree Of Freedom ◽

Repetitive Motion ◽

Spatial Mechanism ◽

Joint Axis ◽

Specific Geometry ◽

Noncircular Gears ◽

Six Degree Of Freedom ◽

The Given

This paper introduces a reconfigurable one degree-of-freedom spatial mechanism that can be applied to repetitive motion tasks. The concept is to incorporate five pairs of noncircular gears into a six degree-of-freedom closed-loop spatial chain. The gear pairs are designed based on the given mechanism parameters and the user defined motion specification of a coupler link of the mechanism. It is shown in the paper that planar gear pairs can be used if the spatial closed-loop chain is comprised of six pairs of parallel joint axes, i.e. the first joint axis is parallel to the second, the third is parallel to the fourth, …, and the eleventh is parallel to the twelfth. This paper presents the detailed reverse kinematic analysis of this specific geometry. A numerical example is presented.

The Design of a Single Degree of Freedom Open-Loop Spatial Mechanism That Incorporates Geared Connections

Volume 4: Design and Manufacturing ◽

10.1115/imece2009-12806 ◽

2009 ◽

Cited By ~ 1

Author(s):

Joseph M. Bari ◽

Carl D. Crane ◽

David B. Dooner ◽

Javier Roldan Mckinley

Keyword(s):

Numerical Optimization ◽

Closed Loop ◽

Three Dimensional ◽

Open Loop ◽

Degree Of Freedom ◽

Single Degree Of Freedom ◽

Variable Parameters ◽

Spatial Mechanism ◽

Repetitive Tasks ◽

Position And Orientation

A means has been discovered to apply gear pairing to create a one degree of freedom open-loop spatial mechanism. A specially chosen geometry consisting of three pairs of parallel joint axes is constricted by five sets of gears, three of which are parallel planar, allows for a reconfigurable mechanism that is suited for repetitive tasks. Previous work has examined three-dimensional rigid body guidance in closed-loop geared mechanisms, but has not come to a solution for the open-loop case. Gear pairs are designed based upon a desired position and orientation path for the end effector. Numerical optimization is performed to obtain physically realizable gear profiles. Non-circular gear centrodes must be continuous and smooth as well as mono-directional, that is, gear ratios of a given pair may not switch signs. These constraints eliminate non-realizable or non-optimal gears in favor of simple, more easily produced profiles. Variable parameters include link lengths, joint offsets and twist angles. Numerical examples are presented.

On the elimination of branching in the synthesis of spatial single-loop mechanisms with lower pairs

Robotica ◽

10.1017/s0263574700003969 ◽

1988 ◽

Vol 6 (2) ◽

pp. 149-154

Author(s):

George N. Sandor ◽

Yongxian Xu ◽

Tzu-Chen Weng

Keyword(s):

Closed Loop ◽

End Effector ◽

Single Loop ◽

Spatial Mechanism ◽

The Relationship ◽

Motion Generator ◽

Loop Motion

SUMMARYA single-loop spatial mechanism kinematically becomes an open robot, if we separate the grounded joint of the input link which may then be considered as the end effector of the robot. Any position of the end-effector within the workspace of such an open robot can be reached via a number of different configurations of the links. These configurations are called “branches” of the open robot for that particular position of the end effector.If the open robot is now stretched to a limiting position by a force exerted on the end effector, all the possible branches of the mechanism approach each other. When they become coincident, they form the “limiting configuration”. Any two related branches are at opposite sides of the limiting configuration. From the relationship between the links in th elimiting configuration and in related branches, conditions for aviodance of branching of the original closed-loop mechanism can be obtained. This is necessary in order to assure that a set of consistent relative displacements are specified for the open robot to move displacements are specified for the open robot to move toward the desired end-effector position without jumping from one branch to another. As for the closed-loop mechanism, open robot branching aviodance ensures that a desired sequence of positions of a particular floating link in the loop will be generated without changing the branch of the link configuration.In this paper, the above approach is applied to RSSR, RRSC, RRSRR, RRRRRRR and RPCRRR spatial closed-loop motion-generator mechanisms and the corresponding conditions for aviodance of branching in the synthesis of the mechanisms are derived.

Six-degree-of-freedom pose estimation with µm/µrad accuracy based on laser multilateration

Journal of Sensors and Sensor Systems ◽

10.5194/jsss-10-19-2021 ◽

2021 ◽

Vol 10 (1) ◽

pp. 19-24

Author(s):

Jan Nitsche ◽

Matthias Franke ◽

Nils Haverkamp ◽

Daniel Heißelmann

Keyword(s):

Pose Estimation ◽

Coordinate Measuring Machine ◽

Degree Of Freedom ◽

End Effector ◽

Data Rates ◽

Measurement Principle ◽

Measuring Machine ◽

Six Degree Of Freedom ◽

Adequate Measurement

Abstract. The estimation of the six-degree-of-freedom position and orientation of an end effector is of high interest in industrial robotics. High precision and data rates are important requirements when choosing an adequate measurement system. In this work, a six-degree-of-freedom pose estimation setup based on laser multilateration is described together with the measurement principle and self-calibration strategies used in this setup. In an experimental setup, data rates of 200 Hz are achieved. During movement, deviations from a reference coordinate measuring machine of 20 µm are observed. During standstill, the deviations are reduced to 5 µm.

22nd Biennial Mechanisms Conference: Robotics, Spatial Mechanisms, and Mechanical Systems ◽

Structural Parameters Which Reduce the Number of Manipulator Configurations

10.1115/detc1992-0235 ◽

1992 ◽

Author(s):

Constantinos Mavroidis ◽

Bernard Roth

Keyword(s):

General Class ◽

Inverse Kinematics ◽

Structural Parameters ◽

Degree Of Freedom ◽

Characteristic Polynomials ◽

End Effector ◽

Lower Maximum ◽

Abstract The inverse kinematics of series-chain, six-degree-of-freedom manipulators has been developed to the point where it yields all possible configurations for a given end-effector position and orientation. In this paper we use the methods of inverse kinematics to uncover the conditions on the structural parameters which cause a manipulator to yield a lower maximum number of configurations than its general class. It is shown that the following conditions can cause a diminution In the maximum number of possible configurations: parallel joint axes, perpendicular joint axes, intersecting joint axes, and Bennett geometries. Using these geometries in 6R, 5R1P, 4R2P and 3R3P chains, this paper determines the reduction in degree of their characteristic polynomials.

A novel method for recording the position and orientation of the end effector of a spatial cable-suspended robot and using for closed-loop control

The International Journal of Advanced Manufacturing Technology ◽

10.1007/s00170-014-5681-2 ◽

2014 ◽

Vol 72 (5-8) ◽

pp. 739-755 ◽

Cited By ~ 5

Author(s):

M. H. Korayem ◽

H. Tourajizadeh ◽

M. Taherifar ◽

S. Khayatzadeh ◽

M. Maddah ◽

...

Keyword(s):

Closed Loop ◽

Closed Loop Control ◽

End Effector ◽

Loop Control ◽

Novel Method ◽

Position And Orientation

Teaching Manipulator Kinematics by Painting With Light

Volume 6: 35th Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2011-47670 ◽

2011 ◽

Cited By ~ 1

Author(s):

Michael Shomin ◽

Jonathan Fiene

Keyword(s):

Inverse Kinematics ◽

Three Dimensional ◽

Robotic Manipulators ◽

Video Camera ◽

Robotic Arm ◽

End Effector ◽

Teaching Platform ◽

Manipulator Arm ◽

Servo Controller ◽

In this paper, we examine the creation and benefits of a new teaching platform to introduce and reinforce the key concepts of robotic manipulators in an introductory-level robotics course. This system combines a vintage PUMA 260 six-degree-of-freedom robotic arm with modern control circuitry and a Matlab API. The API operates as a servo controller for the robot, thereby allowing students to apply their knowledge of inverse kinematics to a real manipulator arm. To further motivate the exploration of manipulators, we have developed an open-ended project where students engage in the art of three-dimensional light painting. To facilitate this activity, a tricolor LED has been affixed to the end-effector of the robot. With a digital SLR camera, we take a long-exposure photograph as the robot is driven through a trajectory, effectively painting a picture with the end effector. We have also developed a method to quickly assemble pseudo-long-exposure photographs and videos using an inexpensive video camera. We believe this novel setup and project are an effective way to engage and motivate students to learn the underlying math and dynamics of robotic manipulators.

Accurate Motion of a Robot End-Effector Using the Curvature Theory of Ruled Surfaces

Journal of Mechanisms Transmissions and Automation in Design ◽

10.1115/1.3258934 ◽

1988 ◽

Vol 110 (4) ◽

pp. 383-388 ◽

Cited By ~ 7

Author(s):

B. S. Ryuh ◽

G. R. Pennock

Keyword(s):

Trajectory Planning ◽

Interpolation Method ◽

Ruled Surface ◽

Degree Of Freedom ◽

End Effector ◽

Straight Path ◽

Curvature Theory ◽

Six Degree Of Freedom ◽

Differential Properties

In robotics, there are two methods of trajectory planning: the joint interpolation method which is appropriate for fast transition of the robot end-effector; and the cartesian interpolation method which is appropriate for slower motion of the end-effector along straight path segments. Neither method, however, is sufficient to allow a smooth, differentiable, transition of position and orientation of the end-effector. In this paper, we propose a method of trajectory planning that will permit more accurate motion of a robot end-effector. The method is based on the curvature theory of a ruled surface generated by a line fixed in the end-effector, referred to as the tool line. The orientation of the end-effector about the tool line is included in the analysis to completely describe the six degree-of-freedom motion of the end-effector. The linear and angular properties of motion of the end-effector, determined from the differential properties of the ruled surface, are utilized in the trajectory planning.

Structural Parameters Which Reduce the Number of Manipulator Configurations

Journal of Mechanical Design ◽

10.1115/1.2919373 ◽

1994 ◽

Vol 116 (1) ◽

pp. 3-10 ◽

Cited By ~ 29

Author(s):

C. Mavroidis ◽

B. Roth

Keyword(s):

General Class ◽

Inverse Kinematics ◽

Structural Parameters ◽

Degree Of Freedom ◽

Characteristic Polynomials ◽

End Effector ◽

Lower Maximum ◽

The inverse kinematics of series-chain, six-degree-of-freedom manipulators has been developed to the point where it yields all possible configurations for a given end-effector position and orientation. In this paper we use the methods of inverse kinematics to uncover the conditions on the structural parameters which cause a manipulator to yield a lower maximum number of configurations than its general class. It is shown that the following conditions can cause a diminution in the maximum number of possible configurations: parallel joint axes, perpendicular joint axes, intersecting joint axes, and Bennett geometries. Using these geometries in 6R, 5R1P, 4R2P, and 3R3P chains, this paper determines the reduction in degree of their characteristic polynomials.

Time suboptimal control of industrial manipulators along specified paths while keeping an end-effector orientation unchanged

Robotica ◽

10.1017/s0263574702004629 ◽

2003 ◽

Vol 21 (2) ◽

pp. 153-161 ◽

Cited By ~ 2

Author(s):

S. Kilicaslan ◽

Y. Ercan

Keyword(s):

Suboptimal Control ◽

Time Step ◽

End Effector ◽

Industrial Manipulator ◽

Industrial Manipulators ◽

Angular Velocities ◽

System Equations ◽

Six Degree Of Freedom ◽

Time Suboptimal Control

A method for the time suboptimal control of an industrial manipulator that moves along a specified path while keeping its end-effector orientation unchanged is proposed. Nonlinear system equations that describe the manipulator motion are linearized at each time step along the path. A method which gives control inputs (joint angular velocities) for time suboptimal control of the manipulator is developed. In the formulation, joint angular velocity and acceleration limitations are also taken into consideration. A six degree of freedom elbow type manipulator is used in a case study to verify the method developed.