Research Papers

Linkage-Based Analysis and Optimization of an Underactuated Planar Manipulator for In-Hand Manipulation

[+] Author and Article Information
Aaron M. Dollar

Yale University
New Haven, CT 06520

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received August 1, 2012; final manuscript received August 21, 2013; published online November 6, 2013. Assoc. Editor: Qiaode Jeffrey Ge.

J. Mechanisms Robotics 6(1), 011002 (Nov 06, 2013) (9 pages) Paper No: JMR-12-1108; doi: 10.1115/1.4025620 History: Received August 01, 2012; Revised August 21, 2013

This paper investigates the in-hand manipulation capabilities of a compliant, underactuated planar robotic hand by treating the system as a simple, symmetric, 6-bar linkage mechanism with compliant joints. Although underactuated hands are generally not considered to be adept at dexterous tasks, we have found through past work that an underactuated manipulator can control n degrees of freedom with n actuators by leveraging the passive compliance to satisfy contact constraints on the object. Assuming the system to be quasi-static, the workspace of the underactuated mechanism is found through constraint-based energy minimization by sweeping through the set of allowable inputs. In this study, we investigate achievable workspaces by exploring the nondimensionalized design space, consisting of linkage ratio, joint stiffness ratio, transmission ratio, base linkage length, and object linkage length. The results of this study are useful in motivating the design of dexterous, underactuated manipulators, as well as to predict the achievable workspace of specific hand/object configurations.

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Grahic Jump Location
Fig. 1

Underactuated SDM hand motivating this study on dexterity

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Fig. 2

Basic pseudorigid body model for the SDM finger

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Fig. 3

When an object deflects the SDM finger from its unloaded configuration, passive compliance from the loaded joints can apply a closing force on the object

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Fig. 4

Closed kinematic chain representation of the planar manipulation problem. Assuming contact constraints hold, the system can be viewed as a 6-bar linkage.

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Fig. 5

Sample kinematic workspace for linkage with parameters LP = LD = 0.5, LB = 0.25, LO = 0.5. Greater intensity in topmost plot indicates more achievable orientations at that x–y location

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Fig. 6

Cartesian kinematic workspace coverage for varying Lr, LB, LO parameter values. Higher intensity indicates that parameter combination results in greater coverage of the workspace.

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Fig. 7

Stationary singularities for the 6-bar closed chain. Setting bounds on the actuation constraints ensure that underactuated manipulator never reach these unstable configurations.

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Fig. 8

Comparison of full (left) versus usable (right) kinematic workspaces for parameters LP = LD = 0.5, LB = 0.25, LO = 0.5. As in Fig. 5, top-most Cartesian workspace has higher intensity at x–y locations with greater degree of achievable orientation.

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Fig. 9

Underactuated workspaces for object length LO = 0.2. First column utilizes parameter values from exemplar SDM hand. Second column utilizes parameters from configuration optimal in orientation. Third column utilizes parameters from configuration optimal in Cartesian workspace. Proportion of coverage in Cartesian xy space is denoted by pc, coverage in orientation is denoted by pz.

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Fig. 10

Workspaces for underactuated manipulation linkage with respect to linkage ratio for a selection of initial joint positions

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Fig. 11

Close-up of Cartesian workspace from Fig. 9, where LP/LD = 1.5, LB = 0.27, K = 0.24, R = 1, showing how internal force on the object linkage varies according to position. Internal force is normalized with respect to the maximum internal force measured for this workspace.

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Fig. 12

Contour plots detailing the reachable calculated Cartesian workspaces for the range of system parameters, averaged over all object sizes

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Fig. 13

Contour plots detailing the calculated achievable orientations for the range of system parameters, averaged over all object sizes



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