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Research Papers

Passively Driven Redundant Spherical Joint With Very Large Range of Motion

[+] Author and Article Information
Louis-Thomas Schreiber

Laboratoire de robotique de l'Université Laval,
Département de génie mécanique,
Université Laval,
Québec, QC G1V 0A6, Canada
e-mail: louis-thomas.schreiber.1@ulaval.ca

Clément Gosselin

Professor
Fellow ASME
Laboratoire de robotique de l'Université Laval,
Département de génie mécanique,
Université Laval,
Québec, QC G1V 0A6, Canada
e-mail: Clement.Gosselin@gmc.ulaval.ca

Manuscript received October 18, 2016; final manuscript received January 12, 2017; published online March 23, 2017. Assoc. Editor: Raffaele Di Gregorio.

J. Mechanisms Robotics 9(3), 031014 (Mar 23, 2017) (10 pages) Paper No: JMR-16-1324; doi: 10.1115/1.4035802 History: Received October 18, 2016; Revised January 12, 2017

This paper presents a novel passive redundant spherical joint with a very large range of motion. A kinematic model is first developed in order to provide a framework for the analysis. The principle of the redundant joint is then introduced. The proposed joint does not require any active component since the redundancy is passively handled using springs. A static model of the joint is developed in order to clearly demonstrate how all singularities or jamming configurations can be avoided. Two possible arrangements are presented, one using linear springs and one using a torsional spring. Finally, experimental prototypes are demonstrated that can attain a range of tilt angle of ±150 deg.

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References

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Figures

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Fig. 1

cad model of a 9dof kinematically redundant parallel robot. Six spherical joints are used to connect the legs to the moving platform.

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Fig. 2

Kinematically redundant leg (2(UPR)-S), where U stands for a Hooke joint, P stands for a prismatic joint, R stands for a revolute joint and S stands for a spherical joint. Underlined joints are actuated.

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Fig. 3

Example of a 6dof platform with one kinematically redundant leg whose spherical joint is in a large tilt angle position. An enlargement of the spherical joint and the redundant link is shown.

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Fig. 4

Generic spherical joint and definition of the azimuth (α) and tilt (β) angles

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Fig. 5

Standard Hooke joint with forks (1 and 3) and cross (2)

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Fig. 6

Workspace of a typical Hooke joint. The limitations are due to mechanical interferences.

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Fig. 7

Kinematic chain (4R) representing the redundant spherical joint

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Fig. 8

Workspace of a Hooke joint with one elongated fork

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Fig. 9

Special joint with only two local minima. The effect of angle θ1 (rotation of the first joint) is also shown.

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Fig. 10

Simplified representation of the passive redundant spherical joint with revolute joints represented by cylinders. Linear springs are included in order to control the redundancy and avoid singular configurations.

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Fig. 11

Effective torque on θ1 generated by the linear springs

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Fig. 12

Neutral position (straight lines forming an ‘X’), contact limits (closed region bounded by a solid line), and singular configurations (dots) for the redundant spherical joint using linear springs for reorientation

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Fig. 13

Three-dimensional visualization of the orientation of segment AH at mechanical contact limits (light cylinder) and intersection of the neutral configuration space with the mechanical contact space (dark cylinder)

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Fig. 14

Neutral positions of the spherical joint using a torsional spring for reorientation. Stable positions are represented by the darker surface and unstable positions by the lighter surface. The vertical axis corresponds to the first joint angle θ1while the (r, θ) coordinates correspond to the tilt and azimuth (β, α) like in the other polar plots.

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Fig. 15

Neutral position (vertical line), unstable equilibrium (horizontal line), and mechanical contact limits (closed region) of a spherical joint using a torsional spring for reorientation and with two elongated forks

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Fig. 16

Neutral position (vertical line), unstable equilibrium (horizontal line), and mechanical contact limits (closed region) of a spherical joint using a torsional spring for reorientation and with a special contact geometry

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Fig. 17

Contact initiated between the upper fork's (5) pin (3) and the lower fork's (1) protrusion (2) for the joint using a torsional spring

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Fig. 18

Enlargement of Fig. 16. Two cases in which unstable equilibrium (horizontal line) is kept until mechanical contact (wavy line). The dot represents the joint configuration. (a) rebound on an incorrectly oriented area and (b) smooth surface and no second contact.

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Fig. 19

cad model of the linear-spring-joint prototype. Identified parts are 1: lower fork, 2: linear spring, 3: cross, 4: cable 1, 5: upper fork, 6: cable 2.

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Fig. 20

Prototype of a 4R redundant spherical joint using linear springs for passive reorientation

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Fig. 21

Prototype of a 4R redundant spherical joint using a torsional spring for passive reorientation

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Fig. 22

Torsional spring joint prototype at the contact limit configuration

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Fig. 23

Torsional spring joint prototype at maximum tilt angle configuration

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