Ron P. Podhorodeski

Kinematic Analysis and Optimization of a New Three Degree-of-Freedom Spatial Parallel Manipulator

A study of the kinematic characteristics of a three degree-of-freedom (dof) parallel mechanism is presented. The architecture of the mechanism is comprised of a mobile platform attached to a base through three identical prismatic-revolute-spherical jointed serial linkages. The prismatic joints are considered to be actuated. These prismatic actuators lie on a common plane and have radial directions of action. The mechanisms inverse displacement solution is obtained. Since the mechanism has only 3 dof, constraint equations describing the inter-relationship between the six motion coordinates are derived. These constraints allow the definition of parasitic motions, i.e., motions in the three unspecified motion coordinates. Architecture optimization of the device is undertaken demonstrating that specific values of design variables allow minimization of parasitic motion.

A family of stewart platforms with optimal dexterity

Stewart platform configurations (architectures and poses) optimizing local dexterity are investigated. The condition number of the Jacobian matrix is used to quantify the dexterity of the manipulator. For a platform-centered Jacobian reference location and a given characteristic length for scaling purposes, a two-parameter family of optimal configurations is shown to exist. Two suitable architectural parameters defining the family are identified and properties of the optimal configurations are discussed. The optimization results are shown to be easily extended for other Jacobian reference locations and for other singular value-based local dexterity measures. It is suggested that the existence of a two-parameter family of optimal local configurations could be exploited to aid in the resolution of optimal architectures for global measures.

Resolving redundant manipulator joint rates and identifying special arm configurations using Jacobian null-space bases

Joint rate solutions for redundant manipulators are formulated in terms of a particular solution and a homogeneous solution formed using a basis for the Jacobian null space. Solutions for several local optimization objectives are formulated in terms of Jacobian null-space bases. A method based on a decomposition of screw coordinates is presented for finding null-space bases and particular solutions. The screw decomposition is applied in the derivation of the analytical expressions for the null-space bases and in the identification of special configurations for a seven-revolute manipulator. The analysis is then extended to multiple-arm systems with common degrees of freedom, and is applied to an analytical example involving industrial manipulators mounted on a common platform. >

An Explicit Method for Determining the Force-Moment Capabilities of Redundantly Actuated Planar Parallel Manipulators

A new explicit methodology for the determination of the force-moment capabilities of nonredundantly and redundantly actuated planar parallel manipulators (PPMs) is presented. This methodology is based on properly adjusting the actuator outputs to their maximum capabilities. As a result, the wrench to be applied or sustained is maximized. For a nonredundantly actuated PPM, one actuator can be maximized, while for a redundantly actuated PPM, one actuator, beyond the one of the nonredundant case, may be maximized for every degree of redundancy added to the mechanism. This methodology is compared to a previous work that required an optimization algorithm. The new method yields more accurate and reliable results and is considerably more efficient. Four studies of force-moment capabilities are considered: maximum force with prescribed moment, maximum applicable force, maximum moment with a prescribed force, and maximum applicable moment. The methodology is used to generate the force-moment capabilities of an existing PPM throughout its workspace.

Reciprocity-based resolution of velocity degeneracies (singularities) for redundant manipulators

Abstract A methodology for determining the velocity-degenerate (singular) configurations of joint-redundant manipulators is presented. The developed methodology uses the properties of reciprocal screws to determine all degenerate configurations resulting in a single degree-of-freedom (DOF) motion loss. Six joint screws (

Wrench capabilities of planar parallel manipulators. part i: Wrench polytopes and performance indices

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Forward displacement analysis and uncertainty configurations of parallel manipulators with a redundant branch

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Optimization-Based Synthesis of Grashof Geared Five-Bar Mechanisms

sub6) are chosen to form one six-joint sub-group Jacobian, J sub . Setting the determinant of J sub to zero ( | J sub |=0 ) allows all conditions (say n in total) that cause the six-joint sub-group to become velocity degenerate to be identified. Reciprocal screws, W recip 1 , W recip 2 ,…, W recip n , can be found for each of the n velocity-degeneracy conditions. The reciprocal screw, W recip i , is reciprocal to the six joints that comprise J sub when the ith J sub degeneracy condition is true, but will not necessarily be reciprocal to the redundant joints

Workspace analysis of a 3-DOF parallel mechanism

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Complete forward displacement solutions for a class of three-branch parallel manipulators

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