Problem $1.[5$ Marks$]$

For the coordinate systems established in Figure, if $l_i=ID(000000$uarruarr$+150)mm,k_2=ID(000000$uarruarr$+180)mm,d_3=ID(000000$uarruarr$+130)mm,{}_1=ID(0000000$uarr$+20),{}_2=ID(0000000$uarr$+30)$ and ${}_3=ID(0000000$uarr$+10).$ Using D$-$H calculate the $44$ homogeneous transformation matrices $H_1^0,H_2^1,H_3^2,$ and $H_3^0=H_1^0**H_2^1**H_3^2.$

Problem $2.[5$ Marks$]$

For the coordinate systems established in Figure, if $l_{\text{I}}=ID(000000$uarruarr$+120)mm,d_1=ID(0000000$uarr$+23)mm,{}_1=ID(0000000$uarr$+36{)}^o,k_z=ID(000000$uarruarr$+128)mm,{}_2=ID(0000000$uarr$+42),l_3=ID(0000000$uarr$+57)$ mm and ${}_3=ID(0000000$uarr$+65).$ Using D$-$H calculate the $44$ homogeneous transformation matrices $H_1^0,H_2^1,H_3^2,$ and $H_3^0=H_1^0**H_2^2**H_3^2.$