Synthesis of three-revolute spatial chains for body guidance

Hauenstein, Jonathan D.; Wampler, Charles W.; Pfurner, Martin

doi:10.1016/j.mechmachtheory.2016.12.008

Cited by 13 publications

(5 citation statements)

References 20 publications

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“…Since kinematic synthesis problems, such as path synthesis and motion generation [9,17], are classical but challenging problems that yield polynomial systems [28], the following provides some related work using numerical algebraic geometry [4,26]. A variety of homotopy methods have been used to solve a collection of synthesis problems, such as [10,15,20,27]. The estimation method in [19] uses a coupon collector model based on the success ratio of finding new solutions using parameter homotopies [18].…”

Section: Related Workmentioning

confidence: 99%

Using monodromy to statistically estimate the number of solutions

Hauenstein¹,

Sherman²

2020

Preprint

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Synthesis problems for linkages in kinematics often yield large structured parameterized polynomial systems which generically have far fewer solutions than traditional upper bounds would suggest. This paper describes statistical models for estimating the generic number of solutions of such parameterized polynomial systems. The new approach extends previous work on success ratios of parameter homotopies to using monodromy loops as well as the addition of a trace test that provides a stopping criterion for validating that all solutions have been found. Several examples are presented demonstrating the method including Watt I six-bar motion generation problems.

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Section: Related Workmentioning

confidence: 99%

Using monodromy to statistically estimate the number of solutions

Hauenstein¹,

Sherman²

2020

Preprint

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“…Cervantes-Sanchez et al [12] analyze a spatial linkage with two loops; however, it does not have the RRR spatial serial chain that characterizes our system. Hauenstein et al [13] focus on the design of spatial RRR serial chains to guide an end-effector along a desired trajectory, however, this mechanism has three degrees-of-freedom. This is the first presentation of a synthesis theory for a RRR-2SS spatial linkage to coordinate the joint angles of the RRR spatial chain.…”

Section: Literature Reviewmentioning

confidence: 99%

Synthesis of a Flapping Wing Mechanism Using a Constrained Spatial RRR Serial Chain

Wang

Taha

McCarthy

2017

Journal of Mechanisms and Robotics

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This paper designs a one degree-of-freedom (1DOF) spatial flapping wing mechanism for a hovering micro-air vehicle by constraining a spatial RRR serial chain using two SS dyads. The desired wing movement defines the dimensions and joint trajectories of the RRR spatial chain. Seven configurations of the chain are selected to define seven precision points that are used to compute SS chains that control the swing and pitch joint angles. The result is a spatial RRR-2SS flapping wing mechanism that transforms the actuator rotation into control of wing swing and pitch necessary for hovering flight of a micro-air vehicle.

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“…The finite-position synthesis of the spatial 3R chain was partially solved in [15,16]. In [17], interval analysis was applied to obtain a set of solutions for the exact synthesis problem, and in [18], numerical algebraic geometry was used to obtain the number of solutions of the problem and to numerically solve the set of equations, which are based on a vector formulation. While algebraic solutions for the finite-position synthesis of spatial chains tends to be a very complex problem, it is possible to state a simpler set of equations for the mixed-position synthesis.…”

Section: Introductionmentioning

confidence: 99%

Mixed Position and Twist Space Synthesis of 3R Chains

Hassanzadeh

Pérez-Gracia

2022

Robotics

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Mixed-position kinematic synthesis is used to not only reach a certain number of precision positions, but also impose certain instantaneous motion conditions at those positions. In the traditional approach, one end-effector twist is defined at each precision position in order to achieve better guidance of the end-effector along a desired trajectory. For one-degree-of-freedom linkages, that suffices to fully specify the trajectory locally. However, for systems with a higher number of degrees of freedom, such as robotic systems, it is possible to specify a complete higher-dimensional subspace of potential twists at particular positions. In this work, we focus on the 3R serial chain. We study the three-dimensional subspaces of twists that can be defined and set the mixed-position equations to synthesize the chain. The number and type of twist systems that a chain can generate depend on the topology of the chain; we find that the spatial 3R chain can generate seven different fully defined twist systems. Finally, examples of synthesis with several fully defined and partially defined twist spaces are presented. We show that it is possible to synthesize 3R chains for feasible subspaces of different types. This allows a complete definition of potential motions at particular positions, which could be used for the design of precise interaction with contact surfaces.

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Synthesis of three-revolute spatial chains for body guidance

Cited by 13 publications

References 20 publications

Using monodromy to statistically estimate the number of solutions

Using monodromy to statistically estimate the number of solutions

Synthesis of a Flapping Wing Mechanism Using a Constrained Spatial RRR Serial Chain

Mixed Position and Twist Space Synthesis of 3R Chains

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