On Planar Five-bar Motion Generation with a Driver Torque Constraint

Abstract

In motion generation, the objective is to calculate the mechanism parameters required to achieve or approximate a set of prescribed rigid-body positions. 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 a conventional planar five-bar motion generation model, planar five-bar mechanisms are synthesized to not only achieve prescribed rigid-body positions, but also satisfy maximum driver torque for a given rigid-body load.

On the Synthesis of Spatial RRSS Motion Generators with Prescribed Coupler Loads

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AbstractThis work extends the concepts and methodologies of Shen et al (1) and Al-Smadi et al (2) to synthesis of spatial RRSS motion generators with applied coupler loads. A general four-bar mechanism constraint that includes a coupler static load and a driver static torques is formulated using the principal of virtual work.

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“…The concept of motion generation with static coupler loading for planar four-bar mechanisms has been addressed by Huang and Roth (11) with analytical motion generation models and recently by Shen et al (1) and Al-Smadi et al (2,12) with numerical motion generation models. This work extends the concept of motion generation with static coupler loading to consider one of the most basic spatial four-bar mechanisms-the RRSS mechanism.…”

“…Equation (8) defines the rotation of the R-R link moving pivot joint axis about its fixed pivot joint axis (the angular displacement of the R-R link). Given three prescribed coupler poses, Equations (1)∼(6) form a set of 12 design equations to calculate the 12 unknown variables in a 0 , a 1 , u 0 and u 1 .…”

“…Formulating Equations (5), (6) and (9) poses and satisfy the maximum crank static torque condition for a given couple load are calculated. Like the works of Shen et al (1) and Al-Smadi et al (2) , the authors employ Sequential Quadratic Programming (SQP) for solving the nonlinear optimization problems. Equation (21), the general SQP merit function used by Han (14) and Powell (15) , includes Equation (20) as the objective function, Equations (1)∼(4) as equality constraints (variable m e ) and Equation (19) and an inequality constraint (variable m) for the first nonlinear optimization problem.…”

“…Equation (21), the general SQP merit function used by Han (14) and Powell (15) , includes Equation (20) as the objective function, Equations (1)∼(4) as equality constraints (variable m e ) and Equation (19) and an inequality constraint (variable m) for the first nonlinear optimization problem. The reader could refer to the works of Shen et al (1) and Al-Smadi et al (2) for detailed SQP algorithm steps.…”