| Summary: | This paper proposes a classification of all non-isomorphic anatomies of an orthogonal metamorphic manipulator according to the topology of workspace considering cusps and nodes. Using symbolic algebra, a general kinematics polynomial equation is formulated, and the closed-form parametric solution of the inverse kinematics is obtained for the coming anatomies. The metamorphic design space was disjointed into eight distinct subspaces with the same number of cusps and nodes plotting the bifurcating and strict surfaces in a cartesian coordinate system <inline-formula> <math display="inline"> <semantics> <mrow> <mrow> <mo>{</mo> <mrow> <msub> <mi mathvariant="sans-serif">θ</mi> <mrow> <msub> <mi mathvariant="sans-serif">π</mi> <mn>1</mn> </msub> </mrow> </msub> <msub> <mrow> <mrow> <mo>,</mo> <mi mathvariant="sans-serif">θ</mi> </mrow> </mrow> <mrow> <msub> <mi mathvariant="sans-serif">π</mi> <mn>2</mn> </msub> </mrow> </msub> <msub> <mrow> <mrow> <mo>,</mo> <mi mathvariant="normal">d</mi> </mrow> </mrow> <mn>4</mn> </msub> </mrow> <mo>}</mo> </mrow> </mrow> </semantics> </math> </inline-formula>. In addition, several non-singular, smooth and continuous trajectories are simulated to show the importance of this classification.
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