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Research Papers

Geometric Design With Multiple Realizable Motion Tasks in the Vicinity of a Planar Mechanism–Environment Contact

[+] Author and Article Information
Nina Robson

Associate Professor
Department of Mechanical Engineering,
California State University,
Fullerton, CA 92834;
Associate Researcher
Mechanical and Aerospace Engineering,
University of California,
Irvine, CA 92697
e-mail: nrobson@fullerton.edu

Binyun Chen

Department of Mechanical Engineering,
California State University,
Fullerton, CA 92834
e-mail: binyunchen@csu.fullerton.edu

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received October 8, 2018; final manuscript received April 26, 2019; published online May 17, 2019. Assoc. Editor: Ashitava Ghosal.

J. Mechanisms Robotics 11(4), 041007 (May 17, 2019) (11 pages) Paper No: JMR-18-1357; doi: 10.1115/1.4043687 History: Received October 08, 2018; Accepted April 26, 2019

This paper applies geometric design principles to planar mechanical systems, attempting to explain complex motion in mechanism–object/environment interaction for realizing multiple kinematic tasks in the vicinity of a contact location. The latter is a critical feature not fully captured in existing design methodologies. This is achieved through the development of a general planar geometric model that allows the derivation of multiple velocity and acceleration specifications compatible with mechanism–object curvature constraints in the vicinity of the contact. By incorporating these higher-order kinematic specifications into the design task formulation, contemporary planar kinematic synthesis is generalized allowing robust designs. The results are illustrated by the kinematic synthesis of two planar revolute–revolute (RR) linkages that are able to push and roll-slide along the object’s curvature in the vicinity of a contact location, a hybrid hand that incorporates a four-bar prosthetic finger that is able to grasp objects in two different modes, and a six-bar orthotic wheelchair for disabled canines that integrates body tilt and climbing motions.

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Figures

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Fig. 1

Planar multidirectional contact task geometry example: for each motion direction n = 1, 2, it is assumed that the contact of the moving body M with two virtual objects constrains the trajectories of points An and Bn to follow circles in the vicinity of a specified position. The point trajectories A(t)n and B(t)n are with known radii of curvature RAn and RBn. Note that n is a function of the active degrees of freedom of the mechanism. The resulting velocity poles for each contact motion are denoted by Vn.

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Fig. 2

The planar multidirectional contact task geometry example from Fig. 1, incorporating the two inflection circles, related to the velocity poles Vn, n = 2, associated with the two directions. Points inside each of the inflection circles Vn have trajectories that curve away from the pole and those outside of the circle have trajectories that curve toward the pole.

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Fig. 3

The task specification, consisting of one position with two velocities and two accelerations

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Fig. 4

The movement of the two synthesized planar RR mechanisms G1W1 and G2W2 for two realizable motions in the vicinity of a contact location. Each trajectory is related to a velocity and acceleration specification v, a, compatible with contact and curvature constraints between the mechanism and the convex object with known contact curvature. The centers of curvature in the vicinity of the contact frame are denoted by On and Cn, where n = 1, 2.

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Fig. 5

Closer look at the trajectories of each RR chain, as well as the two inflection circles with centers D1 and D2, related to the velocity poles V1 and V2, respectively

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Fig. 6

An example of the two RR fingers G1W1 and G2W2 roll-sliding (left) and pushing (right) on an object with a known curvature in the vicinity of a contact. Due to higher-order motion specifications, the two fingers are synthesized to maintain known contact curvatures and constraint forces with the object.

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Fig. 7

The four-bar linkage is able to achieve the originally specified task in two different modes, shown on the left and right hand sides, respectively, each of which related to one of the desired motion directions

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Fig. 8

The two modes of the designed four-bar prosthetic thumb. The previously designed anthropometric planar four-bar orthotic wearable thumb (on the left hand side) is connected and drives the synthesized prosthetic thumb (on the right hand side) through a passive mechanism.

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Fig. 9

The resulting six-fingered hybrid hand holding a ball with a diameter of 27.5 cm in one mode and another heavier ball with a diameter of 22 cm in the another mode. Both balls cannot be grasped and held with one hand. The prosthetic finger is able to successfully maintain contact curvatures and constraint forces with the large objects in both modes.

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Fig. 10

The four-bar linkage is able to achieve the originally specified two wheel submotion tasks

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Fig. 11

CAD drawing of the passive wheelchair with traced wheel climbing, as well as body sit–sniff tilt trajectories

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Fig. 12

The 3D printed orthotic wheelchair resulted in climbing abilities of more than two times the wheel diameter

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Fig. 13

The wearable 3D printed orthotic wheelchair is easily attachable/removable

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