Objective

Develop an extended 5-bar kinematic linkage design for the FHD that optimizes the design for maximum force output over the entire workspace, while satisfying the constraint of fitting the stochastic workspace of the human finger and any mechanical assembly constraints.

Work Status/Results

The maximum force output of a mechanism varies with kinematic parameters, mechanism configuration (i.e., location in the workspace), and direction of applied force. The minimum force in a given configuration taken over all directions in a plane is proportional to the inverse of the maximum singular value of the mechanism Jacobian matrix for that configuration. As part of the optimization process, we searched the entire reachable workspace of each candidate mechanism for the minimum force value. The mechanism with the highest minimum force value was judged the best design.
A drawing of the extended 5-bar mechanism is shown below:

The actuators for the mechanism are on the A1 and B1 joints only; the remaining joints are free-motion joints with the exception of the Theta-B3 joint, which is a fixed kinematic parameter of the mechanism (part of the blue link in the figure above). The design parameters of this mechanism are as follows:

Link Length Min Angle Max Angle
A1 A1_LEN A1_THETAMIN A1_THETAMAX
A2 A2_LEN A2_THETAMIN A2_THETAMAX
A3 B3_LEN A3_THETAMIN A3_THETAMAX
B1 B1_LEN B1_THETAMIN B1_THETAMAX
B2 B2_LEN B2_THETAMIN B2_THETAMAX
B3 B3_LEN B3_THETAVAL
D_AB: DAB_LEN

Thus there are a total of 17 parameters that describe the kinematic design of the extended 5-bar mechanism. We can significantly reduce this parameter space by making the following observations and assumptions:

Due to design limitations for the flat-coil actuators, we set the motion range of A1 and B1 to be 90 degrees.
Since A2 and B2 are free-motion joints, we assign them a motion range of [0,160] and [-160,0] degrees respectively. This single-sided motion range will simplify the design of the free-motion joints and provides a workspace with a reduced number of interior singularities.
We similarly set the motion range of A3 to be in range, [-180,90] degrees.
It can be shown that the singular values of the (x,y) velocity Jacobian are proportional to uniform scaling of the 5-bar mechanism link lengths. Thus our optimization criteria will scale inversely with uniform link length scaling. For this reason, we can optimize for some normalized-length mechanism and then scale the optimal design to fit our workspace requirements. We define the total A linkage path (A1+A2+A3) as a constant 100 units. We then vary the total length of the B linkage path (B1+B2+A3) relative to the A linkage path as one of the kinematic design parameters (note that A3=B3 must be true for the extended 5-bar mechanism).
These observations and assumptions allow us to reduce our design space from 17 to 8 parameters for the design optimization process.
A range of discrete values were chosen for each of these 8 parameters, and a combinatorial search of the design space was performed using 10-12 computers running in parallel over a period of about 36 hours. The kinematic structure of this solution is shown below; it was used as the basis of the mechanical design process.