Kevin Russell

Kinematic synthesis of adjustable RRSS mechanisms for multi-phase motion generation

This paper presents a new technique for synthesizing RRSS mechanisms to achieve phases of coupler positions using the same hardware. This paper considers two- and three-phase problems with constant and adjustable crank and follower lengths. By specifying the joint axes of the RRSS mechanism, the constant length condition becomes the only design constraint. Coupler body positions are then selected with respect to the specified joint axes. These positions are incorporated in the constraint equation and the RRSS mechanism joint variables calculated.

Kinematic synthesis of RRSS mechanisms for multi-phase motion generation with tolerances

Abstract This paper presents a new technique for synthesizing spatial RRSS mechanisms to achieve phases of both precise rigid body positions and rigid body positions with tolerances. This method is an extension of the adjustable RRSS motion generation synthesis method developed by the authors [11]. By incorporating rigid body point tolerances in the rigid body displacement matrices and calculating mechanism solution loci for the prescribed rigid body positions under the tolerance limits, circle and center point regions can be calculated. R–R link solutions can then be selected from these regions. This paper considers two-phase fixed and moving pivot adjustment problems with fixed and adjustable crank and follower lengths.

Kinematic Synthesis of Adjustable RSSR-SS Mechanisms for Multi-Phase Finite and Multiply Separated Positions

This paper presents a new technique for synthesizing RSSR-SS mechanisms to achieve phases of rigid body positions, velocities and accelerations using the same hardware. This work considers two-phase fixed pivot adjustment problems with fixed crank and follower lengths. By specifying the R-S link joint axes, the constant length condition becomes the only design constraint for these links. The prescribed finite and multiply separated positions are then incorporated in the link constraint equations with respect to the prescribed coordinate frame for each link and the RSSR-SS mechanism joint variables and driving link parameters are calculated.

Instant screw axis point synthesis of the RRSS mechanism

Abstract This paper presents a precision point synthesis of the RRSS motion generator, by specifying a set of successive points to the instantaneous screw axis. The method involves synthesizing RRSS mechanisms to achieve prescribed crank and coupler displacement angles by incorporating instant screw axis (ISA) points in the fixed axode point polynomial and calculating the R–R and S–S link parameters of this mechanism. The synthesis is facilitated by specific geometry of the RRSS mechanism, where the fixed axode is calculated as intersection of the R–R member plane and the S–S member axis. The RRSS fixed axode point polynomial was developed using the Cosine law approach introduced by Muller [Kansas State University Special Report No. 21, June 1962]. Complete expansion of the developed RRSS fixed axode point polynomial reveals that it is of order 56.

Expanded spatial four-link motion and path generation with order and branch defect elimination

This work addresses the inverse problems of expanded motion and path generation for the spatial (revolute–revolute–spherical–spherical, RRSS) linkage and the 4R spherical linkage with order and branch elimination. Two constrained non-linear equation systems are presented in this work for RRSS and 4R spherical motion and path generation with order and branching constraints. Both equation systems include the spatial four-link displacement model (by Suh and Radcliffe) as an objective function along with order and branching inequality constraints. As examples, both a branch defect-free and order defect-free RRSS linkage 4R spherical linkage are synthesized to approximate expanded groups of precision positions.

Planar Four-Bar Motion Generation with Prescribed Static Torque and Rigid-Body Reaction Force#

Abstract In motion generation, the objective is to calculate the mechanism parameters required to achieve or approximate a set of prescribed rigid-body poses. This work introduces a new design constraint that considers driving link static torque for a given rigid-body load. By incorporating this new constraint into conventional planar four-bar motion generation models (Sandor and Erdman, 1984; Suh and Radcliffe 1978), planar four-bar mechanisms are synthesized to achieve not only prescribed rigid-body poses, but also to satisfy prescribed driver static torque for a given rigid-body load. The included example demonstrates the synthesis of a four-bar braking mechanism.

Kinematic Synthesis of Planar Four-Bar Mechanisms for Multi-phase Motion Generation with Tolerances

Abstract This article presents a new technique for synthesizing planar four-bar mechanisms to achieve phases of both precise rigid body positions and rigid body positions with tolerances. This method is an extension of the adjustable RRSS motion generation synthesis methods developed by the authors. (Russell, K., Sodhi R. S. (2001). Kinematic synthesis of adjustable RRSS mechanisms for multi-phase motion generation. Journal of Mechanism and Machine Theory 36:939–952; Russell K., Sodhi R. S. (2002). Kinematic synthesis of adjustable RRSS mechanisms for multi-phase motion generation with tolerances. Journal of Mechanism and Machine Theory 37:279–294.) By incorporating rigid body point tolerances in the rigid body displacement matrices and calculating mechanism fixed and moving pivot solution loci for the prescribed rigid body positions under the tolerance limits, circle and center point regions were calculated. The circle and center points for the crank and follower link solutions for the planar four-bar mechanism were selected from these regions. In this article, two-phase moving pivot adjustment problems with constant crank and follower lengths are considered.

On cam system design to replicate spatial four-bar mechanism coupler motion

The coupler motion of a planar four-bar mechanism can be reproduced by rotating the mechanisms moving centrode over its fixed centrode. For spatial four-bar mechanisms, coupler motion can be replicated by moving the mechanisms moving axode over its fixed axode in a screw motion – a combination of simultaneous rotations and translations. This study presents a model to calculate the fixed and moving axodes of the revolute–revolute–spherical–spherical (RRSS) mechanism – one of the most basic spatial four-bar mechanisms. The axodes are useful in producing the contact surfaces for a cam system to replicate RRSS coupler motion.

On the application of CAD technology for the synthesis of spatial revolute-revolute dyads

This work presents a method based on Computer Aided Design or CAD for facilitating the synthesis of Revolute-Revolute (R-R) dyads with adjustable moving pivots. The CAD-based method presented in this work ensures that all prescribed rigid-body parameters used to synthesize the R-R dyad satisfy particular kinematic requirements of an R-R dyad. Through the application of this CAD method, five of the six general R-R dyad constraint equations are satisfied and therefore not essential for the synthesis of the R-R dyad. By reducing the number of dyad design constraints from six to one, the user can synthesize R-R links with adjustable moving pivots for multi-phase motion and path generation applications. The example included demonstrates the use of the CAD method in the synthesis of an RRSS path generator with adjustable moving pivots.

Planar Four-Bar Motion Generation With Static Structural Conditions

A planar four-bar motion generation model that also includes static structural conditions is formulated and demonstrated in this work. Using this model, planar four-bar motion generators are also synthesized with respect to static torque, deflection constraints, and buckling constraints for a given rigid-body load.