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In this paper, analysis and design of an underactuated compliant variable strokemechanismare
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presented by employing its pseudo-rigid-body model (PRBM). During the design two cases are
considered: prescribed output loading and constant input torque. It is shown that this
mechanism is suitable where variable stroke is required corresponding to variable output
loading. It is also observed that this mechanism is capable of providing nearly constant force
over awide range of input. The analysis and design approaches introduced in this study are also
applicable for other similar underactuated compliant mechanisms.8421
© 2010 Elsevier Ltd. All rights reserved.Compliant mechanisms have been investigated by many researchers because they are less expensive, lighter, and easier
to manufacture when compared to rigid-link mechanisms [1]. Especially in recent years, the interest in the field of
compliant mechanisms has grown steadily [2–9]. One disadvantage of compliant mechanisms is the complexity of their analysis and
design. In order to simplify their analysis, the pseudo-rigid-bodymodel technique (PRBM) has been frequently used in the literature [1].
If the number of small-flexural pivots of a compliant mechanism is increased so that the degree-of-freedom is more than one,
the design of the resultingmechanismbecomes quite challenging. In recent years several studies have been done onmulti degree-
of-freedomcompliantmechanisms [10–13].Moreover,multi degree-of-freedommechanismswill be underactuated if the number
of input to the mechanism is less than its degree-of-freedom. This condition introduces an additional complexity to the design of
such systems. The analysis of underactuated multi degree-of-freedom mechanisms is not as simple as that of one degree-of-
freedom mechanisms. For such mechanisms, kinematic analysis must be performed along with a force analysis. Therefore, the
analysis and design of these mechanisms can be performed by assigning a specific output-loading condition. Kinematics of
underactuated mechanisms is related to their loading conditions as well as link proportions. There are several studies on
underactuated mechanisms: a mechanical logic element with multi-port lever has been investigated by Söylemez and
Freudenstein [14]. Laliberte and Gosselin [15] carried out a study on simulation and design of under actuatedmechanical hands in
which the principle of underactuation that leads to shape adaptation of the hand is introduced and a review of the existing
underactuatedmechanical hands is provided. Tanık and Söylemez [16] derived a synthesis procedure for a variable structure using
two different types of seven-link underactuated mechanisms. Mahindakar, Rao, and Banavar [17] presented a study on control of
an underactuatedmanipulator. Finally, Cheng, Carbone and Ceccarelli [18] studied an underactuated finger operation. The variable
stroke mechanism also possesses constant force characteristics. Several authors made significant contributions in the area of
compliant mechanism with constant force transmission characteristics [19,20].
This paper focuses on the analysis and design of a two degree-of-freedomunderactuated compliant variable strokemechanism
by employing its PRBM. An analysis procedure is set up for the underactuatedmechanism. Amethodology for generalization of the
mechanism is introduced. Design charts are prepared for given output loading and constant input torque. To the best of our
knowledge, this paper is the first to apply such a design approach.
2. Analysis of the variable stroke mechanism
In Fig. 1a, the partially compliant variable stroke mechanism and its PRBM (Fig. 1b) are shown. This mechanism has one input
(the crank) and output (the slider). Therefore, the degree-of-freedom of the mechanism is two while the number of inputs is one.