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Research Papers

Optimal Design of Safe Planar Manipulators Using Passive Torque Limiters

[+] Author and Article Information
Meiying Zhang

Département de Génie Mécanique,
Université Laval,
Québec, QC G1V 0A6, Canada
e-mail: meiying.zhang.1@ulaval.ca

Clément Gosselin

Département de Génie Mécanique,
Université Laval,
Québec, QC G1V 0A6, Canada
e-mail: gosselin@gmc.ulaval.ca

Manuscript received October 28, 2014; final manuscript received March 24, 2015; published online August 18, 2015. Assoc. Editor: Pierre M. Larochelle.

J. Mechanisms Robotics 8(1), 011008 (Aug 18, 2015) (11 pages) Paper No: JMR-14-1309; doi: 10.1115/1.4030273 History: Received October 28, 2014

This paper presents a synthesis approach to build safe planar serial robotic mechanisms for applications in human–robot cooperation. The basic concept consists in using torque limiting devices that slip when a prescribed torque is exceeded so that the maximum force and the maximum power that the robot can apply to its environment are limited. In order to alleviate the effect of the change of pose of the robot on the joint to Cartesian force mapping, it is proposed to include more torque limiters than actuated joints. The design of isotropic force modules is addressed in order to produce proper force capabilities while ensuring safety. The proposed isotropic module of torque limiting devices leads to such characteristics. In addition to modeling the contact forces at the end-effector, the forces that can be applied by the robot to its environment when contact is taking place elsewhere along its links are also analyzed as well as the power of potential collisions. Examples of manipulator architectures and their static analysis are given. Finally, the design of a spatial serial manipulator using the isotropic planar force modules developed in the paper is illustrated.

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Figures

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Fig. 5

Square achievable force space of isotropic force module designs

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Fig. 4

Locus of the isotropic force limitation modules in the design space

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Fig. 3

Force mapping of a planar 2DOF manipulator

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Fig. 7

Achievable force polygons in some configurations of the manipulator with three torque limiters (where ρ = 2/2, γ = 1, τmax,1 = Fmin‖r1,max‖, l1 = (1 + 2)2l4)

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Fig. 8

Contact force perpendicular to the links

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Fig. 9

The maximum forces for all links (where ρ = 2/2, γ = 1, τmax,1 = Fmin‖r1,max‖, l1 = (1+2)2l4,l3 = 0.25,τmax,3 = 10)

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Fig. 10

Manipulator with four torque limiters

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Fig. 2

Examples of achievable force polygons for planar manipulators

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Fig. 1

Achievable force limit imposed by one torque limiter for a given configuration (ri is the position vector of the ith joint with respect to the end-effector)

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Fig. 11

End-effector force polytopes for an example case (where ρ = 2/2, γ = 1, τmax,1 = τmax,2 = Fmin‖r1,max‖, l2 = (1 + 2)2l4,l1 = 2l2)

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Fig. 13

The maximum power at the end-effector (where θ·max,1 = 0.5 rad/s,θ·max,3 = 1.2 rad/s)

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Fig. 14

Force polygons corresponding to the points marked in Fig. 13

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Fig. 15

Maximum power for all links with the same parameters as in Fig. 13

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Fig. 16

Uniform force limiter

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Fig. 17

Spatial 3DOF manipulator combining a uniform force limiter and a planar 2DOF four-link manipulator. A vertical prismatic joint at the base provided the vertical motion while the 2DOF planar manipulator provides the horizontal motion.

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Fig. 6

Two-DOF planar manipulator with three torque limiters

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Fig. 12

The maximum force at all points of the four-link manipulator with the scale τmax,4/l4 = 60

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Fig. 18

The achievable force in the vertical direction (Gg is the weight of the four-link manipulator)

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Fig. 19

Achievable spatial force space for some configurations limited between a sphere and a half-sphere whose center is at [0, 0, -Gg] and radii are equal to Fmin and Fmax (different from that of Eq. (36)), respectively

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Fig. 20

An alternative 2DOF planar module

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