Question

Let us name the links starting from below. The various link lengths and masses are as follows.

L1= 6.7 cm m1=0.4kg

L2= 9cm m2=0.2kg

L3=11.1cm m3=0.5kg

L4=7.5 cm m4=0.4kg

Find out the joint configuration for which the gravity vector would have the maximum effect on each joint motor. Does the gravity vector have any effect on the base motor? You can assume that the gravity vector acts at the center of each link. If the gearing ratio on the motor is 670 find out the resultant torque on each motor due to gravity in this configuration?

Solution:

The configuration in which the maximum load acts on each motor is shown below. The gravity acts as an offset axial load for the base motor and does not create any load torque in the direction of rotation for that motor.

For the other motors the Torque load is given by

T4=(m4*L4/2)*9.81=0.4*9.81*0.075/2= 0.147 Nm

Reflected load on the motor= 0.147/Gearing=0.147/670= 0.000219 Nm

T3= (m4*(L4/2+L3)+m3*(L3/2))*9.81= 0.854 Nm

Reflected load on the motor= 0.147/Gearing=0.854/670= 0.00127 Nm

T2=((m2*L2/2)+m3*(L2+L3/2)+m4*(L2+L3+L4/2))*9.81= 1.737 Nm

Reflected load on the motor= 0.147/Gearing=1.737/670= 0.00259 Nm