Computational and theoretical kinematics and robotics
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Kinematic synthesis of spatial linkages and robots
The dimensional synthesis of serial chains determines the physical dimensions such that their end-effector reaches a specified set of positions. The geometric constraints of these chain primitives yield systems of polynomial of total degree ranging from tens to millions. For small problems (total degree in the hundreds), we used resultant elimination method to obtain analytical solutions, which have been integrated into our design software. For larger problems the polynomial homotopy method was found to be effective in finding all of the solutions. For the most difficult cases, parallel homotopy solver POLSYS_GLP was used on supercomputers with thousands of processors. By combining multiple serial chains, we are capable of design parallel robots. This provides a rich opportunity for the invention of devices to provide leveraged spatial movement.
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Classification of a RRSS linkage
According to the rotatability of the two revolute joints, a RRSS linkage can be classified as Crank-Crank, Crank-Rocker, Rocker-Crank and Rocker-Rocker by Grashof's condition. The classification is based on a discriminant system that determines the number of real roots for a quartic polynomial. This result is a generalization of the classification of planar and spherical four bar linkages. See my publication for details. Click here for a Java applet displaying the type map and classification of spatial RRSS linkages.
An example type map of a RRSS linkage An example type map of a RRSS linkage
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Trajectory planning for general spatial platform linkages
This research presents an algorithm for generating trajectories for multi-degree of freedom spatial linkages, termed constrained parallel manipulators. These articulated systems are formed by supporting a workpiece, or end-effector, with a set of serial chains, each of which imposes a constraint on the end-effector. Our goal is to plan trajectories for systems that have workspaces ranging from two through five degrees-of-freedom. This is done by specifying a goal trajectory and finding the system trajectory that comes closest to it using a dual quaternion metric. We enumerate these parallel mechanisms and formulate a general numerical approach for their analysis and trajectory planning. Examples are provided to illustrate the results. See my publication for details.
Example of the trajectory of a 2TPR linkage that approximates a specified trajectory. Example of the trajectory of a 3RPS linkage that approximates a specified movement.
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Motion interpolation
Motion interpolation is based on dual/double quaternion interpolation algorithm by Prof. Jeffery Q. Ge from State University of New York at Stony Brook. A Java implementations of this algorithm has been developed and integrated into my design software SYNTHETICA.
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Kinematic analysis of linkages and robots
This research studies the kinematic analysis of spatial linkages and robots. It is well known that the kinematics problem is essentially a problem of solving polynomial systems. My research focuses on developing highly efficient polynomial solver based on homotopy continuation and resultant elimination methods.
- Forward kinematics of a Platform platform linkage. I applied Dixon's resultant method to solve the forward kinematics of a special Stewart-Gouph parallel platform manipulator. See my publication for details.
- Inverse kinematics of general 6R manipulators. I have developed an inverse kinematics routine for a 6R painting manipulator. Due its special geometric parameters, a closed-form or analytical inverse kinematics is not available. A resultant elimination based algorithm has been developed to compute the the inverse kinematics. See my publication for details.