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The branches of motion in the configuration space of a reconfigurable linkage can intersect in different ways leading to different types of singularities. In the vast majority of reported linkages whose configuration spaces contain multiple branches of motion the intersection happens transversally, allowing local methods, like the computation of its tangent cone, to identify different branches by means of their tangents. However, if these branches are of the same dimension and they intersect tangentially, it is not possible to identify them by means of the tangent cone at the singularity as the tangent spaces to the branches are the same. Although this possibility has been mentioned by a few researchers, whether linkages with this kind of tangent intersection of branches of motion exist is still an open question. In this paper, it is shown that the answer to this question is yes: A local method is proposed for the effective identification of branches of motion intersecting tangentially, and a method for the type synthesis of linkages that exhibit this particular type of singularity is presented.

The manipulating objects of the micron scale are easily damaged, hence the microgrippers, the key components in micro manipulating systems, demand precise force control, plus miniaturized size. In consequence, the constant force microgrippers arise at the historic moment, generally lacking the ability to fit different sizes, however. To avoid the overload damage, apply to multi-size microparts and simplify the control method, a novel two-stage compliant constant force microgripper is proposed in this paper. Based on the negative stiffness effect, this gripper is connected in parallel with a two-stage negative stiffness module and a positive stiffness module. Then, the elliptic integral method and the pseudorigid-body method are both employed to derive the kinetostatic and dynamic performances. Finally, the analytical results are validated. It is observed that two-stage constant forces of 1.33 N in 305.6 µm and 1.11 N in 330.8 µm are acquired.

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