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

2007 ◽  
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.

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

2008 ◽  
Author(s):  
Javier Rolda´n Mckinley ◽  
Carl Crane ◽  
David B. Dooner
Keyword(s):  
Computer Animation ◽  
Closed Loop ◽  
Three Dimensional ◽  
Motion Generation ◽  
Repetitive Motion ◽  
End Effector ◽  
Spatial Mechanism ◽  
Joint Axis ◽  
Position And Orientation ◽  
Six Degree Of Freedom

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.

Kinematic and Workspace Modelling of a 6-PUS Parallel Mechanism

2018 ◽  
Author(s):  
Jérôme Landuré ◽  
Clément Gosselin
Keyword(s):  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Accurate Description ◽  
Transmission Ratio ◽  
Inverse Kinematic Problem ◽  
Jacobian Matrices ◽  
Six Degree Of Freedom

This article presents the kinematic analysis of a six-degree-of-freedom six-legged parallel mechanism of the 6-PUS architecture. The inverse kinematic problem is recalled and the Jacobian matrices are derived. Then, an algorithm for the geometric determination of the workspace is presented, which yields a very fast and accurate description of the workspace of the mechanism. Singular boundaries and a transmission ratio index are then introduced and studied for a set of architectural parameters. The proposed analysis yields conceptual architectures whose properties can be adjusted to fit given applications.

On the Workspace of Closed-Loop Manipulators With Ground-Mounted Rotary-Linear Actuators and Finite Size Platform

1987 ◽  
Author(s):  
Tzu-Chen Weng ◽  
G. N. Sandor ◽  
Yongxian Xu ◽  
D. Kohli
Keyword(s):  
Coordinate System ◽  
Closed Loop ◽  
Finite Size ◽  
Degree Of Freedom ◽  
Moving Coordinate ◽  
Linear Actuators ◽  
Six Degree Of Freedom

Abstract This paper deals with the workspace of a closed-loop manipulator having three rotary-linear (R-L) actuators on ground-mounted cylindric joints, plus three revolute and three spheric pairs [1]. The workspace is defined as the reachable region of the origin of the moving coordinate system embedded in the six-degree-of-freedom platform of the manipulator. The regions in the workspace where the platform can rotate in any direction, cannot rotate or can rotate in only some directions have been defined as complete rotatability workspace (CRW), nonrotatability workspace (NRW) and partial rotatability workspace (PRW). Equations of the workspace of the platform which has a) complete theoretical rotatability and b) nonrotatability (when its center is on the boundary of the workspace) are respectively derived. The reachable region of the center of the platform, where this center remains in a plane with a given platform orientation, is also studied.

Optimization of Mechanism Timing Using Noncircular Gearing

1992 ◽  
Author(s):  
Judd Bernard
Keyword(s):  
Input Function ◽  
Linear Displacement ◽  
Degree Of Freedom ◽  
Output Link ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Noncircular Gears ◽  
The Given ◽  
Crank Mechanism

Abstract A single degree of freedom mechanism whose input link is a crank driven through continuous revolutions will generate output motions dependent upon the inherent mechanism geometry. For example, the slider of a slider-crank mechanism has a linear displacement (the output motion) as a function of the crank rotation (input). Only within the realm of link proportioning can the slider crank output-input function be altered. In this investigation, the continuously rotating crank of a mechanism is rigidly attached to a gear which is one of a pair of externally meshing noncircular gears. By using noncircular gears, it will be shown that the output motion of the given mechanism can be correlated to the rotation of the mating gear to which the crank is not attached. In this fashion, the output link can then be made to execute its motion according to any prescribed law. The above technique has been implemented for the cases of a crank and rocker mechanism and a slider-crank mechanism.

Kinematic Analysis of Spatial Mechanisms Via Successive Screw Displacements

1975 ◽  
Vol 97 (2) ◽  
pp. 739-747 ◽  
Author(s):  
Dilip Kohli ◽  
A. H. Soni
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Closed Loop ◽  
Displacement Velocity ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
Straight Line ◽  
Unified Method

A new, unified method is proposed and demonstrated to conduct kinematic analysis of spatial mechanisms involving revolute, cylindrical, prismatic, helical and spherical pairs. The paper derives the equations for the successive screw displacements, and the equations for pair constraints. Using these equations, closed-form relationships for displacement, velocity and acceleration of single or multi-loop spatial mechanisms are obtained by (1) breaking the mechanism at a critical joint (2) unfolding the mechanism along a straight line (3) providing successive screw displacement at each joint and (4) reassembling the mechanism to form a closed loop. The application of this newly developed approach is demonstrated by considering an example of a two-loop spatial mechanism with revolute, cylindrical and spherical pairs.

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

2009 ◽  
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.

scholarly journals Kinematic analysis of the 3-RPS-3-SPR series–parallel manipulator

Robotica ◽  
2018 ◽  
Vol 37 (7) ◽  
pp. 1240-1266 ◽  
Author(s):  
Abhilash Nayak ◽  
Stéphane Caro ◽  
Philippe Wenger
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
End Effector ◽  
Inverse Kinematics Problem ◽  
Univariate Polynomial ◽  
Six Degree Of Freedom ◽  
Independent Parameters ◽  
Direct Kinematics

SUMMARYThis paper deals with the kinematic analysis and enumeration of singularities of the six degree-of-freedom 3-RPS-3-SPR series–parallel manipulator (S–PM). The characteristic tetrahedron of the S–PM is established, whose degeneracy is bijectively mapped to the serial singularities of the S–PM. Study parametrization is used to determine six independent parameters that characterize the S–PM and the direct kinematics problem is solved by mapping the transformation matrix between the base and the end-effector to a point in ℙ7. The inverse kinematics problem of the 3-RPS-3-SPR S–PM amounts to find the location of three points on three lines. This problem leads to a minimal octic univariate polynomial with four quadratic factors.

Sign in / Sign up

Export Citation Format

Share Document